Gaëtan Burgaud
email: gaetan.burgaud@univ-brest.fr

Danielle Arzur

Lucile Durand

Marie-Anne Cambon-Bonavita

Georges Barbier
email: georges.barbier@univ-brest.fr

Marine culturable yeasts in deep-sea hydrothermal vents: species richness and association with fauna

Keywords:

come

Introduction 36

Yeasts are ubiquitous microorganisms that represent a part of the microbiota in all natural 37 ecosystems such as soils, freshwaters and marine waters from ocean surface to deep-sea. 38

Marine yeasts are divided into obligate and facultative groups. "Obligate marine yeasts" are 39 yeasts that have never been isolated from anywhere else than marine environment, whereas 40 "facultative marine yeasts" are also known from terrestrial habitats (Kohlmeyer and 41 Kohlmeyer, 1979). Based on these definitions, [START_REF] Kohlmeyer | Marine Mycology: The Higher Fungi[END_REF] have 42 examined yeasts occurring in marine environments and have gathered a list of 176 species 43 isolated from diverse marine habitats. Out of those, only 25 were obligate marine yeasts 44 widely represented by the genera Metschnikowia, Rhodosporidium, Candida and Torulopsis.

Seawater carrying dissolved minerals is then emitted from springs. Two major types of 57 emissions have been found. Warm fluids diffuse at temperatures ranging from 6 to 23°C into 58 seawater at 2-4°C when hot vents called black smockers emit hydrothermal fluid at 270-59 380°C [START_REF] Munn | Marine Microbiology -Ecology and Applications[END_REF]. Thermal gradients in hydrothermal vents are so important that just a 60 few centimeters away, the temperature can fall to 2-4°C allowing mesophilic or psychrophilic 61 organisms as well as thermophilic and hyperthermophilic prokaryotes to grow and interact 62 with all biotic or abiotic components of these ecosystems. Dense animal communities cluster 63 around those hot springs. These communities are supported by the chemolithoautothrophic 64 activities of prokaryotes (Jorgensen and Boetius, 2007). 65

The occurrence of fungi (filamentous fungi and yeasts) at deep-sea hydrothermal vents 66 remains an underexplored topic. Over the last years, the interest for the diversity of microbial 67 eukaryotes in these ecosystems emerged using PCR amplification of SSU ribosomal RNA 68 genes and sequence analysis [START_REF] Edgcomb | Benthic eukaryotic diversity in the Guaymas 610 Basin hydrothermal vent environment[END_REF][START_REF] Lopez-Garcia | Autochthonous eukaryotic diversity in hydrothermal 669 sediment and experimental microcolonizers at the Mid-Atlantic Ridge[END_REF]2007). These 69 papers revealed a scarce fungal diversity but some sequences were novel. Only two papers 70 have specifically dealt with fungal diversity at deep-sea hydrothermal vents based on culture-71 dependent methods [START_REF] Gadanho | Occurrence and Diversity of Yeasts in the Mid-Atlantic Ridge Hydrothermal 621 Fields Near the Azores Archipelago[END_REF][START_REF] Burgaud | Diversity of culturable marine 590 filamentous fungi from deep-sea hydrothermal vents[END_REF]. Culturable yeasts 72 affiliated to Ascomycota and Basidiomycota phyla were reported from hydrothermal waters. 73 Some papers assessing fungal diversity at deep-sea vents were also published. Bass et al. 74 (2007) reported the presence of sequences affiliated to Debaryomyces hansenii and novel 75 sequences closed to Malassezia furfur in hydrothermal sediments. Le Calvez et al. (2009) 76 reported that fungal diversity from deep-sea vent animals was widely constituted of sequences 77 affiliated to Chytridiomycota and Basidiomycota phyla. The latter phylum was mostly 78 represented by yeasts with, for example, the Cryptococcus and Filobasidium genera that form 79 dense clusters. 80 81

The occurrence of yeasts in other deep-sea environments has been much more studied. 82 Nagahama et al. (2001b) reported that culturable fungal diversity was dominated by 83 ascomycetous yeasts in surface sediments in water depths exceeding 2000 meters (Candida,84 Debaryomyces, Kluyveromyces, Saccharomyces and Williopsis). Inversely, diversity was 85 dominated by basidiomycetous yeasts on the subsurface of sediments in water depths 86 exceeding 2000 meters and from deep-sea clams, tubeworms and mussels (Rhodotorula,87 Sporobolomyces,Cryptococcus and Pseudozyma). Recent studies have clearly demonstrated 88 that Cryptococcus was the dominant genus sequenced from sediments collected at deep 89 methane cold seeps (Takishita et al., 2006;2007). Those observations are in agreement with Several yeasts mostly isolated from deep-sea sediments represented new species in the 92 Ascomycota or Basidiomycota phyla [START_REF] Nagahama | Kluyveromyces nonfermentans sp. nov., a new 684 yeast species isolated from the deep sea[END_REF]2001a;2003a;2003b;2006a;93 2008). 94

95

In this study, we decided to assess the presence of yeasts at deep-sea hydrothermal vents 96 based on a culture-based approach with an emphasis on yeasts in interactions with the 97 endemic animal fauna thriving in these extreme ecosystems. A recent paper (Gadanho and 98 Sampaio, 2005) has dealt with the diversity of yeasts in deep-sea vent waters but, to our best 99 knowledge, this is the first report of the culturable yeasts isolated from deep-sea animals. 100

Those interactions with the fauna are discussed based on the cultures obtained from the 101 samples collected during different oceanographic the cruises at Mid-Atlantic Ridge, South-102

West Pacific Lau Basin and East Pacific Rise. 103 The deep-sea samples were processed as described by [START_REF] Burgaud | Diversity of culturable marine 590 filamentous fungi from deep-sea hydrothermal vents[END_REF] taking care to 119 avoid contamination in applying strict sterile sampling conditions. 120 121

Materials and methods

Enrichment conditions and isolation 122

The samples were processed directly after the Nautile or ROV recovery. The ollected samples 123 mainly composed of deep-sea hydrothermal vent animals (Rimicaris exoculata and Chorocaris chacei shrimps and Bathymodiolus azoricus mussels) were used to inoculate the 125 GYPS culture medium that led to the best isolation rate during a previous study (Burgaud et 126 al., 2009). This medium contained per liter: glucose (Sigma) 1 g, yeast extract (AES) 1 g, 127 peptone (AES) 1 g, starch (Fisher) 1 g, sea salts (Sigma) 30 g. This medium was 128 supplemented per litre with agar 15 g and chloramphenicol (Sigma) 500 mg, pH was also 129 adjusted to 7.5. Cultures were done aerobically at 4°C, 15°C, 25°C (ambient temperature), 35 130 and 45°C (only during EXOMAR) at atmospheric pressure until fungal strains were 131 visualized. During the MoMARDREAM-Naut cruise, some dissections were realized on 132 board on animal samples in order to investigate the yeast location. 133

Each purified strain from our collection (

Physiological characterization and statistical analysis 139

All experiments were done in triplicate. The yeasts were grown in liquid GYPS broth media. 140

The effect of temperature on growth was determined at 5°C, 15°C, 25°C and 35°C at 30 g.L -1 141 sea salts. The effect of salinity was analyzed modifying sea salts concentrations in media from 142 0 to 60 g.L-1 with steps of 15 g.L-1 at optimal temperature for each strain. Optical densities 143 (OD) were measured at 600 nm with Nanocolor 100D (Macherey-Nagel, Hoerdt, France) at 144 17, 22, 25 and 28 hours of growth under each condition of salinity and temperature. 145 146 DNA extraction and 26S rDNA sequencing 147 DNA of each strain was extracted using FastDNA Spin Kit (MP Biomedicals, Illkirch, 148

France) specific for fungi and yeasts. Amplifications of the D1/D2 region of 26S rDNA were 149 carried out with rDNA primers ITS5 (5'-GGA AGT AAA AGT CGT AAC AAG-3'), LR6 150

(5'-CGC CAG TTC TGC TTA CC-3'), NL1 (5'-GCA TAT CAA TAA GCG GAG GAA 151 AAG-3') and NL4 (5'-GGT CCG TGT TTC AAG ACG G-3') as described by Gadanho & 152 Sampaio (2005). All PCR reactions were performed in 20 µL reaction volumes containing 19 153 µL of 1X PCR Buffer (Promega), 2 mM of MgCl2, 0.2 mM of each dNTPs (Promega), 0.6 154 µM of primers (forward and reverse), 1.25 U of Taq DNA Polymerase (Promega) and 1µL of 155 DNA. The polymerase chain reactions were performed on France). The 156 amplification consisted in an initial denaturation step at 94°C for 2 min, followed by 30 at 72°C. A negative control with sterile distilled water replacing DNA was added. Two kinds 159 of amplification were generated using ITS5-NL4 and NL1-LR6 primers. The amplified DNA 160 fragments were separated by electrophoresis in 0.8% agarose (w/v) gel (Promega) in 0.5X 161 Tris-Borate-EDTA (TBE) Buffer at 90 V for 1h and stained with ethidium bromide. A 162 molecular size marker was used for reference (Lambda DNA/EcoR1+Hind III Markers, 163 Promega). The DNA banding patterns were visualized under UV transillumination and 164 picture files were generated using Gel-Doc 2000 (Biorad, France). 165

The sequencing of the D1/D2 region of the 26S rDNA was then realized using NL1 on the 166 ITS5-NL4 fragments and NL4 on the NL1-LR6 fragments. The sequences were obtained by 167 "Big Dye Terminator" technology (Applied Biosystems). This work was done at 168 "Biogenouest" sequencing facility in the "Station Biologique de Roscoff" (www.sb-169 roscoff.fr). 170

Phylogenetic analyses 171

Sequences were edited and cleaned using Sequencher v 4.8 (Gene Codes). Sequences were 172 then imported to MEGA 4.0 software (Tamura et al., 2007). Each sequence was analyzed in 173 order to find GenBank sequences with close BLAST-N hits [START_REF] Altschul | Basic local alignment search tool[END_REF]. 174

Similarities between sequences were assessed using pairwise distance calculation with 175 MEGA 4.0. The sequences were trimmed to ensure that all sequences had the same start and 176 end-point. All the D1/D2 regions of the 26S rDNA sequences were aligned using ClustalW 177 v.1.83 (Thompson et al., 1994). After visual checking and manual curation, an alignment 178 composed of 62 taxa and 579 characters was analysed for the Bayesian estimation of 179 phylogeny using MrBayes v.3.1.2 software (Ronquist and Huelsenbeck, 2003). A two-million 180 generation option has been set to run the Metropolis-coupled Monte Carlo Markov Chain 181 method (mcmc). After generation 2 000 000, the standard deviation of split frequencies was P 182 = 0.005997 indicating that a convergence had occurred (P-value of < 0.05). The alignment 183 was analysed using MODELTEST v.3.7 (Posada and Crandall, 1998), in order to obtain the 184 more realistic evolutionary model used for phylogenetic analyses (GTR + G model; gamma-185 distribution shape parameter = 0.3978). Phylogeny was then evaluated using two different 186 methods: (i) Bayesian inference with MrBayes v.3.1.2 analysis using 2 000 000 generations 187

and the mcmc method. The tree search included two mcmc searches with four chains (setting 188 default temperature for heating the chains) and a sampling frequency of 100 generations. A 189 'burnin' of 5000 (25% of the 2 000 000 generations/100 sample frequency) was set in order to 190 exclude the first 5000 trees generated. (ii) Maximum likelihood with 100 bootstrap iterations 191 using PHYML [START_REF] Guindon | PHYML online -a web server for fast maximum 627 likelihoodbased phylogenetic inference[END_REF] and the parameters obtained with MODELTEST v.3.7. 192 The final phylogenetic tree topology was realized using MrBayes v.3.1.2 analysis results.

193

Nodes in the tree show Bayesian posterior probabilities and ML bootstraps respectively. 194

Fluorescent probe design and evaluation 195 196

For the detection of yeasts isolated from deep-sea vent animals by FISH, we designed 197 oligonucleotide probes using the Primrose software (http://www.bioinformatics-198 toolkit.org/Primrose/index.html) as described by [START_REF] Ashelford | PRIMROSE: a computer program for generating and estimating 575 the phylogenetic range of 16S rRNA oligonucleotide probes and primers in conjunction with the RDP-II 576 database[END_REF] using a set of high-199 quality, full-length rRNA sequences of probe target organisms. The PrimRose design tool 200 permitted to produce oligonucleotide probes for the three principal clusters of our collection 201 (Table 3). These probes exhibited no mismatches with the target organisms but exhibited 202 mismatches with the next most similar sequences in the GenBank database proving that the 203 designed probes were in silico highly specific. The target sites of newly designed probes were 204 checked for accessibility using the prediction maps based on the 26S rRNA of Saccharomyces 205 cerevisiae [START_REF] Inacio | In situ accessibility of 652 Saccharomyces cerevisiae 26S rRNA to Cy3-labeled oligonucleotide probes comprising the D1 and D2 653 domains[END_REF]. Each probe was in a relative accessible area of the 26S rRNA 206 secondary structure (Fig S1). As it was not possible to test the probes with culture isolates that 207 exhibited zero or one mismatch with the probes, we used an alternative method and tested the 208 probes against all strains from our collection displaying two or more mismatches with the 209 oligonuceotides. All newly designed probes were labelled at the 5' terminus with the 210 fluorescent marker Cy3. All probes were synthesized by (Proligo, France) and stored in sterile 211 distilled water at -20°C. The newly designed probes were checked under in situ conditions 212 with target and non-target species. The universal probe Euk516-Fluorescein (5'-213 ACCAGACTTGCCCTCC-3'; [START_REF] Amann | Phylogenetic identification and in situ detection of individual 569 microbial cells without cultivation[END_REF] and the non-Euk516-Cy3 (5'-214 CCTCCCGTTCAGACCA-3') probes were used as positive and negative control respectively. 215

The average cell brightness was measured using different formamide concentrations from 0 to 216 80% with steps of 10%. Systematic evaluation of the signal intensities was done by recording 217 images of independent visual fields (encompassing at least 100 cells), followed by digital 218 image analysis using the daime software [START_REF] Daims | daime, a novel image analysis program for microbial ecology and 607 biofilm research[END_REF]. During this step, the intensities 219 of the image pixels analyzed enable determination of single cell fluorescence in relative units 220

(RU). 221

Fluorescence In Situ Hybridization byssus of Bathymodiolus azoricus mussels were processed for FISH analyses. Following 224 harvest and dissections, animal subsamples were fixed with 4% paraformaldehyde solution in 225 phosphate-buffered saline (PBS) for 3 hours at 4°C in a dark room. After fixation, tissues 226 were washed three times with PBS and stored at -20°C in a storage buffer containing PBS and 227 96% ethanol (1:1). 228

On membrane filters. The seawater surrounding shrimps (MoMAR08, Rainbow) was sampled 229 in 5 L sterile sampling bags using a peristaltic pump. Immediately after dives, seawater 230 samples for in situ hybridizations were mixed with 3 % formaldehyde (final concentration) 2 231 hours at 4°C. Fixed seawater was then filtered on polycarbonate membranes 0.22 µm 232 (Nuclepore ® , 47 mm diameter; Whatman, Maidstone, Kent, UK) and rinsed with a PBS 2X -233 sterile seawater (v:v) buffer. Then filters were dehydrated using ethanol series (50 %, 80 % 234 and absolute, 3 min each). Dried filters were stored at -20°C until hybridization treatments. 235 Three membranes were treated in this study. The filtered volume was 0.8 L for membrane A, 236 1 L for membrane B and 1.5 L for membrane C. The filtered seawater on membranes A and B 237 was from the same sample. 238

The samples (environmental samples and membrane filters) were cut in squares and paste 239 with one drop of 0.2% low-gelling point agarose (35-40°C) on slides (Menzel-Glaser, 240

Germany). All slides were then dipped in 0.2% agarose and air dried. Samples were then 241 subjected to dehydratation with increasing concentrations of ethanol (50, 80, and

Results

254

Yeast isolation

Naut oceanographic cruise (Table 1). Most of them (6) were cultivated from external face of 291 the mussel shells and more precisely from the byssus that is a network of filaments allowing 292 attachment to rocks. This tangle gathers a lot of particles and organic matter in decomposition 293 (personal observation). Only one yeast was isolated from the interior of a mussel (Mo32). 294 295

Physiological analysis 296 297

Three categories of strains were identified (Table 2) based on the definition of halotolerant 298 and halophilic microorganisms [START_REF] Margesin | Potential of halotolerant and halophilic microorganisms for biotechnology[END_REF][START_REF] Kushner | Life in high salt and solute concentrations[END_REF]. Non halophiles 299 are strains with maximal growth without sea salts and a decreasing growth rate with increased 300 sea salts concentration in media. Halotolerant yeasts are strains able to grow in the absence as 301 well as in the presence of salt. Halophiles required salt for an optimal growth. Regarding 302 halophily, optimal salinities, optimal temperatures and OD measurement, 9 physiological 303 groups were defined. Most of the isolated strains were non halophiles (23 strains) and 304 halotolerant (2 strains, maximal OD at 30 g/l sea salts) growing efficiently at an optimal 305 temperature of 25°C. Four strains had poor maximal growth at 25°C including 1 non 306 halophile, 2 halotolerant (maximal OD at 30 and 60 g/l sea salts) and 1 halophile (maximal 307 OD at 30 g/l sea salts). Three strains had maximal and efficient growth at 35°C, including 1 308 non halophile, 1 halotolerant (maximal OD at 45 g/l sea salts) and 1 halophile (maximal OD 309 at 30 g/l sea salts). 310 311 Identification 312 313 For species identification, a sequence analysis of the D1/D2 domain of the 26S rRNA gene 314 was done (Fig 1). A total of 12 phylotypes was found among the collection of yeasts isolated 315 from deep-sea hydrothermal vents. Eleven phylotypes could be assigned to a known yeast 316 species and one represents a new yeast species. 317 318 Within Basidiomycota, the Sporidiobolales order was the dominant cluster composed of 16 319 strains. A majority of strains (Ex2, Ex3, Ex4, Ex5, Ex6, Ex7, Ex9, Ex11, Ex12, Mo32, Mo35 320 and Mo37) was identified as Rhodotorula mucilaginosa (100% similarity). A large majority 321 of R. mucilaginosa was isolated from deep-sea shrimps ( 14) and the others from deep-sea 322 mussels (2). As member of the Sporidiobolales order, isolates affiliated to Rhodosporidium 323 diobovatum were also isolated (Mo24, Mo33 and Mo38) with 100% similarity. These 3 strains were isolated respectively from Rimicaris exoculata exuviae in decomposition on 325 smocker rocks, Bathymodiolus azoricus and a sponge. One strain isolated from R. exoculata 326 was identified as Sporobolomyces roseus based on 26S rRNA genes (Mo22) with 100% 327 similarity with the reference strain. Four strains (Mo26, Mo27, Mo28 and Mo29) were 328 affiliated to the Filobasidiales order and identified as Cryptococcus uzbekistanensis (100% 329 similarity). These four strains were all isolated from a carbonate colonization module. Finally, 330 one isolate (Mo36) from B. azoricus mussel was identified as Leucosporidium scottii in the 331

Leucosporidiales order. 332

The Ascomycota phylum gathered 9 strains belonging to the Saccharomycetales order. Within 333 this order, 4 strains (Mo20, Mo21, Mo40 and Bio2) isolated respectively from R. exoculata, 334

Mirocaris fortunata, a deep-sea coral and the gills of the gastropod Ifremeria nautilei were 335 identified as Debaryomyces hansenii (100% similarity). Candida atlantica isolates were 336 found in R. exoculata exuviae in decomposition (Mo25) and B. azoricus (Mo31). One strain 337 isolated from a deep-sea sponge (Ex15) was identified as Pichia guilliermondii (100% 338 similarity). Finally, among the Saccharomycetales order, one strain was identified as Candida 339 viswanathii (Bio1) with 100% similarity. One halophilic strain (Mo39) isolated from a deep-340 sea coral represents a new species in the Candida genus and thus was identified as Candida 341 sp. This strain has 95% similarity with the reference sequence of Candida atmosphaerica (23 342 mismatches on 505 bp). Mo30 isolated from Bathymodiolus azoricus was identified as 343 Phaeotheca triangularis (mitosporic Ascomycota) with 100% similarity. In the Dothideales 344 order, one strain (Mo34) isolated from Bathymodiolus azoricus was identified as Hortaea 345 werneckii with 99.98% similarity (one mismatch on 560bp). 346 Sequencing of the 26S rRNA genes indicated the presence of Ascomycota and Basidiomycota 347 in our culture collection. In term of quantity, the phylum Basidiomycota (21) was two times 348 higher than the Ascomycota (11). In term of species richness, ascomycetous yeasts belonged 349 to 7 different clusters while basidiomycetous yeasts belonged to 5 clusters. 350 351

Fluorescence in situ hybridizations 352

We processed numerous assays to detect fungi on deep-sea hydrothermal vent animal samples 353 using different existing fluorescent probes from different databases. The Euk516-Cy3 probe 354 gave positive results on pure cultures but strong background fluorescence on hydrothermal 355 samples led to the renouncement of its use. The probe MY1574 targeting Eumycota 356 organisms [START_REF] Baschien | In Situ Detection of Freshwater Fungi in an 583 Alpine Stream by New Taxon-Specific Fluorescence In Situ Hybridization Probes[END_REF] showed very weak fluorescence on pure cultures. Thus, we decided to design our own probes (Table 3) based on our culture collection that was divided 358 in 3 main clusters: MitoFilo (Cryptococcus / Mitosporic Filobasidiales order), MitoSporidio 359 (Rhodotorula, Rhodosporidium / Mitosporic Sporidiobolales order) and Sacch 360 (Debaryomyces, Pichia / Saccharomycetales order). The probes designed revealed a strong 361 specificity for the target organisms. The optimal conditions for the in situ hybridization 362 protocol use stringent conditions of 20% formamide (Fig S1). 363

Our aim was to check the applicability of the FISH method to the in situ detection of yeasts in 364 deep-sea hydrothermal fauna samples. Hydrothermal body components of endemic shrimps 365 (Rimicaris exoculata) and mussels (Bathymodiolus azoricus) were fixed for FISH 366 experiments directly after dissection. The pieces of shrimps and mussels that gave the higher 367 number of fungi isolation (interior branchiostegites of shrimps and byssus of mussels) were 368 analyzed for yeast cell fluorescence. Although shrimp and mussel samples from Rainbow site 369 led to the highest rate of isolation, no FISH signal was ever observed. The FISH detection 370 limit of 10 3 -10 4 target cells per ml is relatively high [START_REF] Daims | Fluorescence In situ Hybridisation for the Detection of Prokaryotes[END_REF]

Occurrence of yeasts in deep-sea hydrothermal vents 384

In this study, the main aim was to isolate yeast strains from deep-sea hydrothermal endemic 385 fauna knowing that yeasts can be isolated from seawater surrounding hydrothermal fauna 386 [START_REF] Gadanho | Occurrence and Diversity of Yeasts in the Mid-Atlantic Ridge Hydrothermal 621 Fields Near the Azores Archipelago[END_REF]. Yeast isolation was successful even if the retrieved species 387 richness was relatively low. Thirty-two strains were isolated mostly from Rimicaris exoculata shrimps. The association with shrimps is probably favorable for yeasts that could benefit from 389 nutrients due to the water circulation in the gill chamber. Most of our strains were isolated 390 from the Rainbow hydrothermal site which confirms previous results (Gadanho and Sampaio, 391 2005). The Rainbow hydrothermal field hosted in ultramafic rocks is a unique vent enriched 392 in CH 4 , H 2 , CO, Fe and depleted in H 2 S [START_REF] Charlou | Geochemistry of high H2 and CH4 vent 596 fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36j14VN, MAR)[END_REF]. The high yeast isolation ratio 393 may indicate that yeasts thrive in hydrothermal sites depleted in H 2 S. The isolation rate of 394 non-pigmented yeasts on sulfur-free media significantly higher than those on sulfur-based 395 media in a previous study [START_REF] Gadanho | Occurrence and Diversity of Yeasts in the Mid-Atlantic Ridge Hydrothermal 621 Fields Near the Azores Archipelago[END_REF] support such hypothesis. 396 397

Several yeasts were also isolated from mussels and more precisely from the byssus 398 constituted of filaments with a high concentration of minerals and organic matter. These 399 yeasts may have a role in the decomposition of organic material entrapped in mussel byssi in 400 deep-sea vents. These results seem promising as they confirm the data obtained in previous 401 studies and suggest that yeasts may interact with deep-sea hydrothermal vent fauna. 402 403

Pattern of the culturable yeast communities 404

New species. 405

The yeast that was firstly isolated from stomach of a marine fish was described as D. hansenii 406 and deposited in the Centraalbureau voor Schimmelcultures (CBS 5307) database. In a recent 407 paper, based on the intergenic spacer (IGS) region of the rRNA gene, this strain was re-408 evaluated as Candida sp. (Nguyen et al., 2009). This strain is identical to another one isolated 409 from deep-sea hydrothermal vent waters and annotated MARY089 (Gadanho and Sampaio, 410 2005). These two strains isolated from different marine environments were finally reported as 411 a single new undescribed species within the Candida genus. In our collection, strain Mo39, 412 isolated from deep-sea coral near Rainbow hydrothermal vents (Table 1), has the same 26S 413 rRNA gene sequence as CBS 5307 and MARY089. Mo39 is halophilic and thus supposed to 414 be an autochtonous marine yeast species. This new ecotype can be characterized as an 415 obligate marine yeast and its complete description is currently under progress. 416 417

Known species 418

Two strains (Mo25 and Mo31) isolated from Rimicaris exoculata and Bathymodiolus azoricus 419 samples were identified as Candida atlantica. This result seems in keeping with previous 420 published reports that have isolated this species from coastal seawater in the South of 421

Portugal [START_REF] Gadanho | Assessment of yeast diversity in a marine environment in the 615 south of Portugal by microsatellite-primed PCR[END_REF] and in deep-sea hydrothermal vent waters (Gadanho and 422 Sampaio, 2005). The very fisrt C. atlantica strain was isolated from shrimp eggs in the North 423 Atlantic Ocean (Siepmann and Höhnk, 1962). C. atlantica seemed to be a marine obligate yeast and some interactions with shrimps seemed to occur. Our physiological analysis has 425 revealed that Mo25 and Mo31 were non-halophiles, which does not mean that they are unable 426 to grow in marine environments. They may have a role in deep-sea environments in 427 interaction with endemic crustaceans even if they are not in optimal growth conditions. One 428 isolate (Bio1) isolated from seawater surrounding mussels at Lau Basin in the South-West 429 Pacific was clearly identified as Candida viswanathii. [START_REF] Kohlmeyer | Marine Mycology: The Higher Fungi[END_REF] 430 characterized this yeast as marine facultative. More recently, C. viswanathii was isolated from 431 a shrimp (Peneaus braziliensis) in the Gulf of Mexico. Its synonym, Candida lodderae was 432 recently reported in deep-sea hydrothermal vent waters at Rainbow site (Gadanho and 433 Sampaio, 2005) and characterized as the most abundant yeast. 434 435 Leucosporidium scottii isolates (Mo36) were retrieved only in the oceanic regions close to 436 Antarctica and are known to be psychrophilic and probably autochthonous marine species 437 [START_REF] Lachance | Ecology and yeasts[END_REF]. Such strains known for their presence in cold polar marine 438 environments could be another evidence that confirms the hypothesis of global exchanges 439 from polar environments to deep-sea vents based on results from bacteria (Maruyama et al., 440 2000) and filamentous fungi [START_REF] Burgaud | Diversity of culturable marine 590 filamentous fungi from deep-sea hydrothermal vents[END_REF]. Hortaea werneckii (Mo34) was 441 characterized as halophilic in our physiological study. This is not surprising as this black 442 yeast-like fungus was characterized as halophilic or extremely halotolerant in different studies 443 [START_REF] Gunde-Cimerman | Hypersaline waters in salterns -natural 630 ecological niches for halophilic black yeasts[END_REF][START_REF] Kogej | The halophilic fungus Hortaea werneckii and 646 the halotolerant fungus Aureobasidium pullulans maintain low intracellular cation concentrations in hypersaline 647 environments[END_REF] where it was frequently isolated from 444 hypersaline waters of solar salterns. In a molecular survey, H. werneckii was identified (based 445 on internal transcribed spacers and 5.8 S rRNA gene) in deep-sea methane seep sediments at a 446 depth of 2965 meters [START_REF] Lai | Fungal communities from methane hydrate-bearing 659 deep-sea marine sediments in South China Sea[END_REF]. Phaeotheca triangularis (Mo30) was also frequently 447 isolated from salted environments [START_REF] Gunde-Cimerman | Hypersaline waters in salterns -natural 630 ecological niches for halophilic black yeasts[END_REF] and characterized as 448 halophile. This confirmed previous results on P. triangularis showing a better growth with 449 5% additional salts (Zalar et al., 1999). In our study, Mo30 was characterized as halotolerant 450 with 4.5% sea salts optimal concentration and thus hypothesized as marine adapted yeast. 451 This is the first report about the presence of Phaeotheca triangularis at deep-sea vents. 452

Mo22 is described as Sporobolomyces roseus. The genus Sporobolomyces is composed of 453 strains mainly isolated from the pyllophane [START_REF] Bai | Reclassification of the Sporobolomyces 579 roseus and Sporidiobolus pararoseus complexes, with the description of Sporobolomyces phaffii sp[END_REF]. However, a previous study has 454 proved that strains of the genus Sporobolomyces are frequently isolated from marine 455 ecosystems and the frequency of isolation increases when distance from the coastline and 456 depth increase [START_REF] Hernandez-Saavedra | Distribution of Sporobolomyces (Kluyver 636 et van Niel) genus in the western coast of Baja California Sur, Mexico[END_REF]. Moreover, yeasts from this genus were 457 found in benthic invertebrates collected from deep-sea floor in the Pacific Ocean (Nagahama Ocean and characterized as halotolerant with an optimal salinity of 6% sea salts. This may 460 indicate that yeasts of this genus are also able to live in deep-sea vents and interact with 461 endemic crustaceans. 462

463

A previous study of yeasts in oceanic environments [START_REF] Fell | Yeasts in oceanic regions[END_REF] reported that yeast 464 communities appeared to be constituted of ubiquitous and endemic species. Typical 465 ubiquitous strains were the ascomycetous yeast Debaryomyces hansenii and the 466 basidiomycetous ones Cryptococcus and Rhodotorula. [START_REF] Kohlmeyer | Marine Mycology: The Higher Fungi[END_REF] 467 confirmed this statement and characterized these genera mainly as facultative marine yeasts. 468 Some of these results, especially for Rhodotorula yeasts showing a strong ubiquity, were 469 confirmed based on their presence in several habitats such as deep-sea vents (Gadanho and 470 Sampaio, 2005), deep-sea sediments (Nagahama et al., 2001b), coastal waters (Gadanho et 471 al., 2003;[START_REF] Zbinden | Yeast isolates resulted from this study were all 286 cultivated from the antero-dorsal area characterized by high amounts of minerals and a dense 287 bacterial mat. 288 289 The yeasts were also isolated from Bathymodiolus azoricus (7) during the MoMADREAM[END_REF] and oligotrophic lakes [START_REF] Libkind | Molecular characterization of 665 carotenogenic yeasts from aquatic environments in Patagonia, Argentina[END_REF]. Our results confirm their 472 ubiquity and indicate that these strains seem to be allochtonous. Strain Ex15 identified as 473 Pichia guilliermondii has also been characterized as non halophile and may be another 474 allochtonous yeast strain as reported by [START_REF] Kohlmeyer | Marine Mycology: The Higher Fungi[END_REF]. 475 476

The members of the genus Rhodosporidum have been characterized as non halophiles (Mo24 477 and Mo33) and halotolerant (Mo38). Based on previous reports, this genus seemed to be 478 restricted to marine environments [START_REF] Gadanho | Occurrence and Diversity of Yeasts in the Mid-Atlantic Ridge Hydrothermal 621 Fields Near the Azores Archipelago[END_REF]. R. diobovatum in deep-sea 479 vents seemed to be able to colonize different substrates (shrimps, mussels and sponges). The 480 isolation of a strain from shrimp exuviae in decomposition may indicate a role as a recycler of 481 organic material and so a probable implication in carbon cycle in deep-sea environments. 482 483

Adaptation to marine conditions 484

The isolation of culturable yeasts led to an old question about marine yeasts "Are there any 485 indigenous marine yeasts ?" [START_REF] Kohlmeyer | Marine Mycology: The Higher Fungi[END_REF] and to the resulting question 486 "Which are the indigenous species ?". Based on our results, one can suggest that halophilic 487 strains are marine indigenous yeasts and that others, halotolerant and non-halophiles, are 488 ubiquitous terrestrial strains present in deep-sea waters due to sedimentation or other natural 489 or anthropogenic phenomena. But almost all yeast species can grow well in media with NaCl 490 concentrations exceeding those normally present in the sea [START_REF] Kohlmeyer | Marine Mycology: The Higher Fungi[END_REF].

Few yeast species with a physiological dependence on NaCl or other seawater components 492 have been reported (Nagahama, 2006b). Thus, our results appeared in good agreement with 493 such statements. Only 2 strains described as halophiles (Mo34 and Mo39) in our study can be 494 described as obligate marine yeasts. 495 FISH observations 496 497 FISH using labeled oligonucleotide probes targeting rRNA has been used as a powerful 498 technique for assessing both microbial identity and spatial distributions in situ in complex 499 environmental contexts (Yang et al., 2008). Our results indicate a very low-level of yeasts at 500 deep-sea vents. As a first conclusion, regarding diversity and quantification (added to 501 previous results of [START_REF] Gadanho | Occurrence and Diversity of Yeasts in the Mid-Atlantic Ridge Hydrothermal 621 Fields Near the Azores Archipelago[END_REF], it seems that yeasts at deep-sea vents 502 represent a minor community that might not be major actors in biogeochemical cycles. 503 However, fluorescent signals are correlated to the cellular content of ribosomes and 504 consequently to the microbial growth rates. Recently, the detection limits of conventional 505 FISH with Cy3-labeled probe EUB338 were found to be approximately 370 16S rRNA 506 molecules per cell for Escherichia coli hybridized on glass microscope slides and 1,400 16S 507 rRNA copies per E. coli cell in environmental samples [START_REF] Hoshino | Quantification of Target Molecules Needed 639 To Detect Microorganisms by Fluorescence In Situ Hybridization (FISH) and Catalyzed Reporter Deposition-640 FISH[END_REF]. So, in addition 508 to a low concentration of yeast cells, low detection of yeasts may be caused by low ribosome 509 content of most yeasts in the deep-sea environment due to low-level metabolic activities of 510 yeasts living under extreme environmental abiotic factors (high hydrostatic pressure, low 511 temperatures,…). Our attempts to cultivate the yeast strains resulted from this study under 512 elevated hydrostatic pressure have been successful, but ribosomal activities were lower under 513 high hydrostatic pressure than at atmospheric pressure. Such results may account for the low 514 fungal detection using FISH (unpublished data). Consequently, care must be taken when 515 dealing with diversity and biomass estimations when using FISH alone. 516

The quantification of yeasts using FISH has been impossible due to a non homogeneous 517 repartition of microorganisms on filters. Moreover, bacterial and yeast cells were only visible 518 in some regions of the filters without minerals due to strong autofluorescence. However we 519 can say that yeast concentrations are really low, as shown by the only few cells visualized 520 after filtration of seawater surrounding shrimps. This result is in keeping with the relatively 521 low diversity revealed by [START_REF] Gadanho | Occurrence and Diversity of Yeasts in the Mid-Atlantic Ridge Hydrothermal 621 Fields Near the Azores Archipelago[END_REF] ranging from 0 to 10 cfu/L for pink 522 yeasts and from 0 to 6000 cfu/L for non-pigmented yeasts. [START_REF] Inacio | In situ accessibility of 652 Saccharomyces cerevisiae 26S rRNA to Cy3-labeled oligonucleotide probes comprising the D1 and D2 653 domains[END_REF]. Each probe was evaluated without formamide in order to check wether the probe binds to the ribosomes of the target cells. The optimal hybridization conditions were determined in a serie of FISH experiments with increasing formamide concentrations for a probe target and a non-target organism : (i) Sacch probe, Debaryomyces hansenii (Target) and Candida atlantica (Non-Target) with two mismatches ; (ii) MitoSporidio probe, Rhodosporidium diobovatum (Target) and Cryptococcus uzbekistanensis (Non-Target) with five mismatches and (iii) MitoFilo probe, Cryptococcus uzbekistanensis (Target) and Rhodosporidium diobovatum (Non-Target) with seven mismatches. Relative probe accessibility was determined for each probe : MitoFilo, about 60%; MitoSporidio and Sacch, 44 to 66%.

  and thus, the absence 371 of FISH signals does not necessarily mean that the target organisms were not present in the 372samples. 373To test this hypothesis, several volumes of water were concentrated on polycarbonate 374 membrane filters to yield sufficient cells for FISH experiments with these new probes. 375Membrane filters were embedded in low gelling-point agarose to minimize cell loss. Yeast 376 cells could be visualized in a low quantity on these membrane filters (Fig2). Such results are 377 another evidence of the yeast cells presence in hydrothermal vents but at low concentration. 378Using FISH on membrane filters, yeast cells detected were affiliated to 3 genera: 379 Rhodosporidium, Rhodotorula and Cryptococcus.

Figure 1 :

 1 Figure1: Phylogenetic tree of deep-sea yeast isolates (coloured terminals) and close relatives obtained by analysis of the D1/D2 domain of the 26S rRNA gene. Topology was built using MrBayes v.3.1.2 from a ClustalW 1.83 alignment. Node support values are given in the following order: MrBayes posterior probabilities/PHYML 100 bootstraps. Black squares represent nodes supported by an excess of 0.95 posterior probabilities and 95% bootstraps. Mucor flavus (EU071390) belonging to the Zygomycota phylum was used as outgroup. All sequences are listed with their GenBank accession numbers.

Figure 2 :

 2 Figure 2: Fluorescence in situ hybridization with specific oligonucleotide probes on membrane filters. (a, b and c) Membrane filter labelled with DAPI and hybridized using MitoSporidio probe indicating the presence of bacteria and yeast cells (blue). Yeasts belonging to Rhodotorula and Rhodosporidium genera are vizualized in pink (composite of blue and red). (d) Membrane filter labelled with DAPI and hybridized with MitoFilo indicating the presence of yeasts belonging to Cryptococcus genera. White arrows indicate the yeast cells.

Figure S1 :

 S1 Figure S1 : Target sites of the fluorescent oligonucleotide probes designed on a model of the Saccharomyces cerevisiae 26S rRNA secondary structure in which the D1 and D2 domains (delimited by NL1 and NL4) are enlarged[START_REF] Inacio | In situ accessibility of 652 Saccharomyces cerevisiae 26S rRNA to Cy3-labeled oligonucleotide probes comprising the D1 and D2 653 domains[END_REF]. Each probe was evaluated without formamide in order to check wether the probe binds to the ribosomes of the target cells. The optimal hybridization conditions were determined in a serie of FISH experiments with increasing formamide concentrations for a probe target and a non-target organism : (i) Sacch probe, Debaryomyces hansenii (Target) and Candida atlantica (Non-Target) with two mismatches ; (ii) MitoSporidio probe, Rhodosporidium diobovatum (Target) and Cryptococcus uzbekistanensis (Non-Target) with five mismatches and (iii) MitoFilo probe, Cryptococcus uzbekistanensis (Target) and Rhodosporidium diobovatum (Non-Target) with seven mismatches. Relative probe accessibility was determined for each probe : MitoFilo, about 60%; MitoSporidio and Sacch, 44 to 66%.

Table 1

 1

	) has been integrated to the 'Souchothèque de

Table 1 .

 1 To better analyze the fungal 523 presence in deep-sea animals, one could work with phylum-specific probes on histological Culture collection of yeasts from deep-sea hydrothermal vents.

	758	Tables and Figures
	759
	760
	761
	762
	763
	764
	765

Table 2 .

 2 Physiological analysis of the yeast collection. This table shows distribution of 796 halotolerant and halophilic strains of the collection depending on their optimal salinities (g/l 797 sea salts), optimal temperatures (°C) and maximal optical densities of cultures on GYPS broth 798 medium (120 rpm on a rotary shaker) measured at 600nm at 4 different incubation times (17h, 799 22h, 25h and 28h).

	800
	801
	802

Table 3 .

 3 Yeast oligonucleotide probes and their sequences, target organisms and binding 806 positions on the 26S rRNA.

	807
	808
	809
	810

Acknowledgements

552

We thank the chief scientists of the BIOLAU, DIVANAUT2, HERO, MARVEL, EXOMAR 553 and MoMARDREAM-Naut cruises, the pilots and support crews of the oceanographic vessels 554

and Deep Submergence Vehicles of Ifremer. We greatly acknowledge Dr Jerome Mounier for 555 his valuable help and comments on FISH and Jerome Lepioufle for valuable advice on the 556 manuscript. We thank all the members of the GDR Ecchis for their advice and suggestions.

557

We would like to thank the editor and the anonymous reviewers who have provided helpful 558 comments on the refinement of this manuscript. We also


Jean-Franc ¸ois Laslier
email: jean-francois.laslier@polytechnique.edu

And the loser is... Plurality Voting

for choosing the best voting rules that was organized among the participants of the Voting Procedures workshop in July, 2010. Among 18 voting rules, Approval Voting won the contest, and Plurality Voting received no support at all.

Introduction

Experts have different opinions as to which is the best voting procedure. The Leverhulme Trust sponsored 2010 Voting Power in Practice workshop, held at the Chateau du Baffy, Normandy, from 30 July to 2 August 2010, was organized for the purpose of discussing this matter. Participants of the workshop were specialists in voting procedures and, during the wrap-up session at the end of the workshop, it was decided to organize a vote among the participants to elect "the best voting procedure". The present paper reports on this vote. It contains in the Appendix statements by some of the voters/participants about this vote and voting rules in general.

The vote

Previous discussion had shown that different voting rules might be advisable under different circumstances, so that a more concrete problem than "What is the best voting rule" should be tackled. The question for the vote was: "What is the best voting rule for your town to use to elect the mayor?" Even with this phrasing, it was realized afterwards that not all participants had exactly the same thing in mind. In particular, some of them were thinking of a large electorate and some were rather thinking of a committee (the city council) as the electorate. This can be inferred from the participants' comments in the Appendix and is clearly a weakness of this "experiment."

Of course, an interesting feature of this vote is the fact that it was a vote on voting rules by voting theorists. So the participants arrived with quite a heavy background of personal knowledge and ideas. But the way the vote was improvised was such that no one had much time to think things over, discuss and coordinate with others, or calculate. Moreover, no candidates were clear common knowledge front-runners, and the final result was apparently not anticipated by most voters.

The possibilities of strategic manipulation were thus quite limited and one can indeed see from the comments that most of these approval votes should be interpreted as the expression of sincere individual opinions. As one referee pointed out: this vote may be the last "naive" vote on voting rules. This adds a particular significance to its result, and also suggests that the experiment should be done again, now that the results are known. 1

Candidates: the voting rules in question

The set of "candidates," that is the list of considered voting rules was rather informally decided: participants just wrote on the paper board voting rules to be voted upon. Eighteen voting rules were nominated, the definitions of which can be found in Appendix 2.

Some rules should really be considered as possible ways to organize elections and will, in usual circumstances, provide indeed a unique winner. Others will often yield not a single winner but a set of possible winners, among which the final choice has to be made by one means or another. The list contains several Condorcetconsistent rules which agree on a unique outcome when the Condorcet winner exists2 but which differ when there is no Condorcet winner and, in that case, often yield several winners. For instance the Uncovered set is a singleton only if there is a Condorcet winner 3 , the Copeland winner is always in the Uncovered set and the Uncovered set is always included in the Top Cycle. The voting rules also differ as to their informational basis.

1. Some of them require very little information: Plurality voting and Majority voting with a runoff simply ask the voter to provide the name of one (or two) candidates. Approval Voting asks the voter to say "yes" or "no" to each candidate. 2. Most rules require that the voter ranks the candidates: this is the classical framework of Arrowian social choice [START_REF] Arrow | Social Choices and Individual Values[END_REF]. There is no inter-personal comparisons of alternatives, which means that the ballots are not intended to convey interpretation of the kind "candidate a is better for voter i than for voter j". The intra-personal structure is purely ordinal, which means that we may know that a is better than b for i, but we cannot know how much better. 3. Finally, some of them allow inter-personal comparisons, with intra-personal comparisons being ordinal (Leximin, Majority Judgement) or cardinal (Range Voting).

Most rules extend the majority principle in the sense that, if there are only two candidates, they select the one preferred by a majority of the voters. Range voting, which maximizes the average evaluation, does not fulfill this principle: indeed, according to classical utilitarianism, if a majority of voters slightly prefer a to b while a minority strongly prefers b to a, it may be better to choose b than a, against the majority principle. Therefore, under Range voting, if voters reflect in their vote this pattern of interpersonal comparisons, the minority candidate b may well be elected against a. Such is also the case for the "Majority judgement" system (despite its name) which maximizes the median evaluation and for the Leximin, which maximizes the worst evaluation.

The procedure

The electorate

The 22 voters were the participants of the workshop (one participant abstained). Some of them are advocates of a specific voting rule; for instance, Ken Ritchie and Alessandro Gardini are active in Great Britain in promoting the "Alternative Vote": a system of vote transfers also known as the "Hare" system. Others, like Dan Felsenthal, are advocates of the Condorcet principle and strongly defended this principle during the workshop. But it is fair to say that most of the participants would say that different voting rules have advantages and disadvantages. This might be one of the reasons why no-one objected to the use of Approval voting for this particular vote.

The voting rule

We used Approval voting for this election. Somebody made the suggestion and there was no counter-proposal. In retrospect, this choice was quite natural: this procedure is fast and easy to use even if the number of candidates is large. Asking voters Number of approvals 0 1 2 3 4 5 6 7 8 9 10 >10 total Number of ballots 0 2 7 3 5 2 1 1 0 0 1 0 22 to rank the 18 candidates was hardly feasible in our case. Approval voting is also advisable when the set of alternatives has been loosely designed and contains very similar candidates 4 . One may nevertheless regret that we lost the occasion to gather, through the vote, more information on the participants' opinions about the different voting rules. Hopefully the next section, where results are presented, will show that we can already learn quite a lot from the analysis of the Approval ballots.

3 The results Approval Voting is the winner of the election. It is worth noticing that it is the only candidate approved by more than half of the voters 5 . Three candidates received no vote at all: Fishburn, Untrapped Set, and Plurality.

Approval score and other indicators

There are actually many different ways to compute scores and other indicators from a set of Approval ballots. Table 3 provides some, which are now defined. The number of voters who approved of both candidates c and c is called the association of c and c , and is denoted by as(c, c ). The number of voters who approved c is denoted by as(c).

Markov score This score is computed as follows.

dil(c) = 1 as(c) ∑ v ∑ k as(v, c, k).
Notice that this indicator can be computed with a formula somehow dual to the focus:

dil(c) = ∑ k as(c, k) as(c) .
The dilution thus measures to what extent supporters of a candidate also vote for other candidates. It should not be interpreted as an indicator of the strength of the candidate but as a part of the description of the electorate of the candidate: do these voters give exclusive support (low dilution), or do they support many other candidates (high dilution).

These indicators are all highly correlated with the approval score, except for the dilution (see Table 4).

App Alt Cop Kem 2R Coo Sim Bal Bor Bla RV Nan Lex TC UC App 15 7 7 4 3 3 4 5 3 3 2 2 1 1 Alt 7 10 2 3 5 4 3 3 1 3 1 1 1 1 Cop 7 2 9 4 1 2 3 4 2 1 0 2 0 0 Kem 4 3 4 8 1 3 3 1 1 1 0 1 0 1 2R 3 5 1 1 6 3 1 1 2 2 0 1 1 0 Coo 3 4 2 3 3 6 1 2 1 1 1 1 0 0 Sim 4 3 3 3 1 1 5 2 2 2 0 2 0 1 Bal 5 3 4 1 1 2 2 5 1 1 1 1 0 0 Bor 3 1 2 1 2 1 2 1 4 1 0 2 0 0 Bla 3 3 1 1 2 1 2 1 1 3 0 1 1 1 RV 2 1 0 0 0 1 0 1 0 0 2 0 0 0 Nan 2 1 2 1 1 1 2 1 2 1 0 2 0 0 Lex 1 1 0 0 1 0 0 0 0 1 0 0 1 0 TC 1 1 0 1 0 0 1 0 0 1 0 0 0 1 UC 1 0 1 1 0 0 1 0 1 0 0 1 0 0

Structure of the set of candidates

Table 5 shows the number of voters who approved each pair of candidates, and Table 6 shows the distribution of these association numbers for each candidate. For instance 7/10 = 70% of the voters who approved the Alternative Vote also approved Approval Voting while 7/15 = 47% of the voters who approved Approval Voting also approved the Alternative Vote. It is interesting to note that 83% of the supporters of two-round majority voting also support the Alternative Vote, but such is the case of only 22% of the Copeland supporters. One may also notice that all the supporters of the Majority Judgement are also supporters of Approval Voting.

To obtain a more global view, one may compute various distances between candidates. Consider for instance for the similarity index

sim(c, c ) = as(c, c ) as(c) + as(c, c ) as(c )
which ranges from 0 (when the electorates of c and c are disjoint) to 2 (when they are identical) and define

dist(c, c ) = 2 -sim(c, c ).
It turns out that there exists a very good Euclidean representation of the 15 candidates in 3 dimensions, that renders 90% of the sum of square of distances. 6 Studying how candidate rules are associated in the voters' ballots, it appears that the winner is receiving votes associated with all the other candidates. Approval Voting can be described as a "centrist" candidate in this vote. Even if one can detect some pattern in the vote profile that differentiates votes for more "theoretical" rules from votes for more "practical" rules, the electorate does not appear to be split.

Conclusion

The analysis of the approval ballots show that Approval Voting was a clear winner of this election. This is somehow surprising since Approval Voting was not much discussed during the workshop. But this voting rule has already received a lot of attention in the academic literature, and was certainly familiar to the participants. A striking fact is that Plurality rule (First Past the Post) received no approval. The whole ranking of the candidate procedures according to their approval scores seems also robust since alternative ways to count the ballots produce rather similar rankings.

Appendix 1: Contributions of the participants

Participants were ex post invited to write a brief statement that would explain their vote and their view about this "election". One-half of them did it, after having read my own contribution (see below) as an example.

It must be acknowledged that, from a scientific point of view, the experimental protocol was a little loose. The nomination procedure for the set of candidate voting rules was informal and voters did not have all the time required to learn everything about all of them. Fuad Aleskerov: "¿From my point of view our voting for the rules was rather spontaneous. For instance, I know more than 30 rules which can be listed for our voting after reading careful studies, by colleagues, of their properties."

It is also worth remarking that, under Approval Voting, it is not so easy to remember after several days or weeks which candidates you approved out of 18.

Marc Kilgour: "I really can't remember very well why I voted the way I did. As I recall, the objective was to propose a system to elect the mayor of a town, without any indication of the number of candidates. I think I assumed that there would not be many. I followed the approval strategy of approving everything that seemed to be above average "utility," whatever that would mean. I voted for approval (my actual favorite) and range because they focus on acceptability rather than ranks. I also voted for two or three others that, it seemed to me, were complicated enough to be likely to produce something that would maximize the sum of the utilities but at the same time sophisticated enough to avoid features I don't like such as non-monotonicity. Beyond that, I can't remember much."

This point holds certainly true, as well, for preference-based balloting: it is not so easy to remember how you ranked the whole set of alternatives; it distinguishes these systems from the familiar single-name Plurality and Two-Round Majority voting rules. The set of received contributions, which follow, show well the variety of view points of the experts in the field.

A. Baujard

The question we have been asked implied to apply the rule in a real political context, involving citizens with their own desires, their own intellectual abilities and the differences among them. Choosing the good rule for a democratic mayor election predicates to pay attention to these features rather than to my own preferences among rules. Through the field-experiments we have conducted, I have learnt that most voters are frustrated by voting rules which gives little scope to the expression of their nuanced preferences, which are sometimes tinted by hesitations, indifference, significant differences between strong vs. weak preferences... These nuances have yet a strong impact on results especially in the case of uninominal voting rules, where a clear cut decision is always required to infer individual preferences. In a democracy, I claim that this should question the legitimacy of the winner in such context. I am therefore not convinced by plurality rules, whatever one or two rounds, Condorcet principle, or any uninominal voting rules in general.

Among plurinominal rules, I focus on the importance of simplicity to explain the rule, and to vote. Above all, I paid attention to transparency, meaning a wide understanding of the process of deriving a result from the ballots, and the ability of citizens to take actively part in the process of counting the votes. These desired properties rule out Alternative Vote, Borda rules and Majority Judgement among others.

Many voters in our experiments spontaneously preferred range voting, begging for the ability of giving negative grades, or a wide range of different grades. Even though this would also be my favorite in an ideal world, I regret how range voting depends on differences in the meaning of grades among people, how it is manipulable -which causes strong inequalities among the voting power of different citizens according to their ability to manipulate. This argument, I admit, may be questionable in a reduced city council, but ruling out range voting seemed cautious in the absence of information on its size and composition.

I have eventually given just one approval in the vote on voting rules : one to approval voting. It is because I had the ability of approving other rules that my choice of giving just one vote was truly meaningful.

D. Felsenthal

I adhere to the Condorcet Principle as a normative principle when one must elect one out of three or more candidates. This principle prescribes that should a candidate defeat every other candidate in pairwise comparisons (a Condorcet winner), it must be elected, and should a candidate be defeated by every other candidate in pairwise comparisons (a Condorcet loser), it must not be elected. This principle conveys the fundamental idea that the opinion of the majority should prevail, at least when majority comparisons pinpoint an unambiguous winner and/or an unambiguous loser. The Condorcet Principle takes into account only the ordinal preferences of every voter between any pair of alternatives because attempting to take into account also voters' cardinal preferences (as under the Range Voting procedure) would not only imply that a Condorcet winner may not be elected or, worse, that a Condorcet loser may be elected, but also that inter-personal comparisons of utility are possible and acceptable -which they are not! I rank all the competing procedures for electing one out of m candidates (m ≥ 2) according to two criteria: First,I prefer all Condorcet-consistent procedures over all procedures that are not Condorcet-consistent. Second, among Condorcet-consistent procedures I prefer those which are not vulnerable to non-monotonicity or to electing a Pareto-dominated candidate when a Condorcet winner does not exist; and among the procedures which are not Condorcet-consistent I prefer those which are not susceptible to one or more of the following four pathologies which I consider as especially serious: non-monotonicity, not electing a candidate who constitutes the top preference of an absolute majority of the voters (aka absolute Condorcet winner), electing a candidate who is a Condorcet loser or is Pareto-dominated.

According to these criteria I approved only Kemeny's and Copeland's procedures because they are both Condorcet-consistent and are not susceptible to any of the above mentioned four pathologies.

My rank-order of the 18 competing procedures is as follows:

Kemeny > Copeland > Black > Nanson > Untrapped Set > Fishburn > Un- covered Set > Top Cycle > Simpson > Borda > Coombs > Alternative Vote > 2-round Majority > Plurality > Majority Judgment > Approval Voting > Leximin > Range Voting.

W. V. Gehrlein

In all honesty, I do not remember exactly which of the many possible rules that were listed that I voted for during this impromptu exercise. However, my general convictions were expressed on the ballot that I submitted. The first statement on my ballot was: "In a perfect world I would recommend any Condorcet consistent voting rule". Standard arguments against the implementation of majority rule based voting are too heavily focused on one atypical example of something that could conceivably happen to ignore an 'almost-majority' minority voting bloc with strong preferences. The obvious question is: What is the likelihood that such a scenario would ever actually exist? We all know that such hypothetical voting situations can always be developed to make any voting rule appear to behave very poorly on some criterion. The only practical way out of this dilemma must therefore be based on the likelihoods that voting rules display such bad behavior. In the context of evaluating voting rules to elect the mayor of a city in a typical situation, my assumption from scenarios that I am familiar with would make the possibility negligible that there would ever be more than four candidates. Since there is a very high probability that a Condorcet winner will exist in such cases, why should we not elect that candidate?

The answer to the immediately preceding question is that Condorcet consistent procedures are not always easy to implement with a larger number of candidates, which led to my second statement on the ballot. "In the real world I would recommend (some elimination rules that I do not recall) and Borda Rule". These rules would give a reasonable probability of electing the Condorcet winner, while also being both explainable to and acceptable to the electorate, without any implication that simplicity should be the only criterion for evaluating voting rules. Arguments about the relatively large probability with which some of these voting rules can be manipulated are typically based on the assumption that one group of voters with similar preferences can manipulate the outcome, while all other voters are completely naive to the situation. When it is further assumed that these other voters are aware of such possibilities and that they can react accordingly, the probability that the winner could actually be changed is significantly reduced. However, it is definitely reasonable to conclude from this exercise that plurality rule is not considered to be acceptable and that Approval Voting is the clear winner when voting is done by Approval Voting. But, it is critical that we must not forget the significant concerns that have been raised about the type of winners that are selected when Approval Voting is employed.

J.-F. Laslier I do not adhere to the Condorcet principle as a normative principle; if 49% of the population strongly prefer A to B and 51% slightly prefer B to A, I think that A is collectively preferable. My first best decision rule is thus utilitarianism, or "range voting". But I found Approval Voting a very good practical mechanism to approximately achieve the utilitarian outcome. For the practice, I find that Condorcetconsistent procedures advisable, except in the extreme but important case of a society split in two. The best Condorcet procedure to me is the randomized procedure studied by B. Dutta, G. Laffond, M. LeBreton and myself under the name Essential set, but this rule was not proposed. In most cases, the Simpson rule (Minmax procedure) is a good way to select in the Essential set, like Kemeny, Coombs, and others. My preference was:

Range > Approval > various Condorcet methods among which I make little difference > Two round plurality > Alternative vote > Leximin > Majority Judgment > Plurality.

My guess was that, for this election, Approval would win, maybe challenged by Alternative vote (I was right !). Therefore I voted for Approval and Range. Here is my complete ranking, with my sincere utilitarian view scaled on the 0-100 scale:

M. Machover

I consider that decision about which voting procedure should be used must be governed by some meta-principle. I also consider that an appropriate meta-principle for the present hypothetical case is majority rule. I therefore gave my approval only to Condorcet-consistent procedures, selecting those that have additional desirable properties: Copeland's and Kemeny's procedures.

V. Merlin

While considering the question "what is the best voting rule that the city council of your town should use to elect a mayor?" my first reaction is that the procedure should be simple and easily understandable by the whole population of the city. The second question to answer is to which degree the Condorcet principle should be implemented. I do not adhere to the Condorcet principle, as a majority of 50% plus epsilon can impose a candidate which is the worst choice of the other voters, without considering compromise candidates. But at least, I do consider that a Condorcet loser should never be elected. Hence, Plurality rule is the worst system in the list.

So, I decided to advise Plurality with 2 rounds, Alternative Voting and Approval Voting. As long as there is a final duel, any elimination system using the plurality tallies will never elect the Condorcet loser. Plurality with two rounds and Alternative Voting are such systems. They are easy to explain, and have been implemented in different countries (France, Australia), with no major complaints. Moreover, Alternative Voting is hardly manipulable. I also consider that k + 1 rounds before the final duel are better than k! Though I also voted for Approval Voting, it may be possible for it to select a Condorcet loser, if everybody just reports his first choice. But I think that the risk is quite limited, provided that a sufficiently large part of the population votes sincerely. Experiences show that voters tend also to approve more than one candidate. What would make me rank Approval Voting slightly below the two previous rules, is the fact that it has not been widely used in political elections. I felt that we still need more real life experiences to check that everything goes right with approval voting, but I am ready to give it its chance.

The simplicity argument goes against many Condorcet-consistent rules. Though Kemeny is an extremely elegant solution to the voting problem, it is rather sophisticated. For those who think that the Condorcet criterion should be implemented, I would recommend the Copeland method, which could be easily explained to the voters, as a tournament among the candidates.

At last, I fear that rules like the Borda count or Range voting could lead to undesired outcomes, when a fraction of the voters tries to manipulate it.

N. Miller

I cast approval votes for Approval Voting and Copeland. My votes did not reflect any general normative principle but rather my sense as to what would be both practical and reasonable for the type of election that Dan Felsenthal stipulated, namely the election of a mayor when a number of candidates are the ballot. A year ago I might have approved of AV/IRV also, but I now think that its problems are quite serious (even in practice, not just in theory). And, as a practical matter, my highest preference would be for Approval Voting, because it is simple to explain to voters, simple to cast votes, and simple to count. Moreover, most voters (in the US at least) would want to see some kind of vote totals in the newspaper the next day, which Copeland does not provide.

While Plurality lost our vote by a landslide, it works perfectly well in most US partisan general elections, since Duverger's Law works so powerfully that there are, literally or effectively, only two candidates in most such elections (the recent Senate contests in Florida and Alaska being notable exceptions). However, Approval Voting might be a definite improvement over Plurality in party primary elections and nonpartisan general elections (which is how many mayors are elected), where often three or more candidates are on the ballot.

Finally, voting procedures need to be evaluated not only in terms of their "static" social choice properties (e.g.,Condorcet consistency, monotonicity, etc.) but also in terms of their "dynamic" effects, e.g., incentives for candidate entry, candidate ideological positioning, etc., which affect the types of preferences profiles that are most likely to arise.

H. Nurmi

We were asked to propose voting systems that we could recommend or approve of to be adopted in the mayoral elections of our municipality. Recommend and approve of are two different -albeit related -things, but since we were asked to submit approval ballots, I felt encouraged to suggest more than one system (which I would NOT do if I were asked to recommend "a system"). I proposed Borda, Nanson and probably also Kemeny (someone may have preempted me on the latter, though). Anyway, my ranking is Nanson > Kemeny > Borda > approval voting and these (as far as I now recall) were on my ballot. Nanson and Kemeny are both pretty resistant to misrepresentation of preferences and take into account a great deal of the preference information given by the voters. (One could also point out that they are Condorcet, but I'm not much moved by that property any longer: some systems are vulnerable to adding or removing or cloning alternatives (e.g. Borda) (as shown by Fishburn), others to adding or removing voters with completely tied preferences (Condorcet)(as shown by Saari). Overall, being based on strict majority principle is not a decisive feature in my book. Although it can be argued that it is preferable to be ruled by a majority than by a minority, I think one should also sail clear of the dictatorship of majority. They (Nanson and Kemeny) both do well in terms of several choice theoretic criteria. Borda's advantage is in intuitively plausible metric rationalizability: it looks for the closest (in terms of inversion metric) consensus profile (in terms of the first ranked alternative) and since we are looking for a single winner, this makes sense. Borda count also does well in minority protection (as shown by Nitzan). Approval voting was also on my ballot, not so much because of its choice-theoretic properties, but because of intuitive appeal of its results: it sounds nice to have a mayor who is deemed acceptable by more voters than any other. I must say, though, that the interpretation of "approvability" is not obvious (and this pertains to the interpretation of our balloting result as well). Does the fact that I approve of a candidate mean that I can tolerate him as the mayor without resorting to active resistance or does it mean that I positively support him/her? I think this is what makes the approval voting results hard to interpret, but I guess a mayor that is even tolerated by more voters than any other candidate has at least tolerable prospects.

F. Plassmann

I view voting as a useful mechanism for making collective decisions when unanimous agreement is not possible. Elections should generally be preceded by discussions about the candidates and the importance that the voters attach to the election. If a minority of voters feels strongly about some candidates while the other voters are almost indifferent between these candidates, then it should be possible for the minority to convince sufficiently many of the others to change their minds prior to the vote-casting process. (I believe that in cases of near-indifference, most people's desire to preserve social harmony trumps rent-seeking.) If it is not possible to change sufficiently many voters' minds, then I would interpret this as evidence that the intensity in preferences between the groups is not as disparate as it might appear. I therefore feel comfortable ignoring voting rules that take account of the intensities of voters' preferences.

I value the Condorcet principle, and I see the main issue as what we should do when there is no Condorcet winner. Apart from the fact that it is not Condorcet consistent, the Borda rule has many attractive properties. Thus my first choice is Black's rule, which seems to be least susceptible, among many popular voting rules, to a wide range of voting paradoxes and which has a very small frequency of ties (as preliminary research with Nic Tideman suggests). The discontinuity of Black's rule also makes strategizing difficult. However, the need to understand two separate evaluation criteria might make Black's rule too complicated for some voters. Voters will accept the outcome of an election only if they understand how the ballots are to be counted. Approval voting is very simple and avoids some of the most egregious shortcomings of the plurality rule. Thus I would endorse approval voting in situations when simplicity is important.

M. Salles

I voted for Approval Voting and for Borda. I share Jean-Franc ¸ois' view regarding the difficulty concerning majority rule. However, I do not go as far as him and would not recommend "range voting". In case there are a sufficient number of candidates, the Borda rule proposes a way to deal somehow with intensity of preferences without going as far as "Range Voting". Also I think that the voting method must be simple enough to be understood by the quasi-totality of the voters, which might not be the case of the alternative vote system or Kemeny's rule.

N. Tideman

A group of experts on voting theory wanted to learn their collective judgments of a variety of voting rules. They decided (by something like acclimation) to proceed by using approval voting. I thought this was a reasonable way of learning the general level of support for different voting rules, as a prelude to future discussion. I would not have recommended approval voting as a way to make a collective judgment of which voting rule is best. That, I think, requires both more time and a procedure for ranking the options, so that direct paired comparisons can be made.

I am quite startled by the high level of support for approval voting as a way of electing a mayor. What I find particularly distressing about approval voting is that it requires a voter to decide whether to draw a line between generally acceptable and unacceptable candidates, or to leave that task to other voters and instead to draw a line between the very best and the close contenders who are not quite as good. I think that voters for a mayor should not be required to choose between drawing those two types of lines.

The relevant criteria for a voting rule for mayor, in my opinion, are:

• First, the capacity of the rule to gain the trust of voters. This depends on the reasonableness and understandability of the logic of the rule and the ease with which the counting process can be followed. Investigating this requires psychological methods as well as knowledge of the logic of voting procedures.

• Second, the likely statistical success of the rule in identifying the outcome with the greatest aggregate utility, under the assumption that voters vote sincerely. This is something that can be investigated by statistical methods.

• Third, the resistance of the rule to strategic voting. This too can be investigated by statistical methods.

It is my guess that the best rule, by some intuitive averaging of these criteria, is the Simpson rule. But the empirical work that would justify this guess remains to be done.

Alternative vote [Alt]

Each voter submits a ranking (possibly incomplete) of the candidates. One first counts the number of times each candidate appears as top-ranked (his plurality score). The candidate with the lowest plurality score is eliminated. In a second count, the votes for this candidate are transferred to the second-ranked candidate (if any) on these ballots. The process is then repeated again and again until one candidate is ranked first by an absolute majority of the votes (original or transferred) is elected. See [START_REF] Farrell | Electoral Systems: A Comparative Introduction[END_REF], [START_REF] Farrell | The Australian Electoral System: Origins, Variations, and Consequences[END_REF]. Other names for this procedure or its variants: "Hare" system, "Single Transferable Vote", "Instant runoff".

Copeland [Cop]

Each voter submits a ranking of the candidates. For each candidate one computes his pairwise comparison score, that is the number of challengers this candidate beats under pair-wise majority rule. The candidates with the largest score are chosen. This Condorcet-consistent rule does not specify how ties (which are common when there is no Condorcet winner) are broken. See [START_REF] Laslier | Tournament Solutions and Majority Voting[END_REF]. Other name: Tournament score.

Kemeny [Kem]

Each voter submits a ranking of the candidates. The rule defines a summary ranking as follows. For any ranking R of candidates one computes the sum, over all pairs (a, b) of candidates of the number of voters who agree with how R ranks a and b. Then R * is chosen to maximize this total number of agreements. The elected candidate is the top-ranked candidate according to R * . This procedure is Condorcetconsistent. See [START_REF] Young | A consistent extension of Condorcet's Election principle[END_REF], [START_REF] Young | Condorcet's theory of voting[END_REF]. Other name: Median ranking.

Two-round majority [2R]

Each voter votes for one candidate. If a candidate obtains an absolute majority, he is elected. If not, a runoff election takes place among the two candidates who obtained the most votes. This rule is the most common rule throughout the world for direct elections, but it has seldom retained the attention of social choice theorists. See Lijphart (1994), Blais, Massicotte, and Dobrzynska (1997), Taagera (2007), Blais, Laslier, Sauger, and Van der Straeten (2010). Other name: Plurality with a run-off.

Coombs [Coo]

Similar to the Alternative Vote but, at each round, if no candidate is ranked first by an absolute majority of the ballots, the eliminated candidate is the one who is most often ranked last. This procedure is Condorcet-consistent in the single peaked domain. [START_REF] Coombs | Theory of Data[END_REF] 7 .

Majority Judgement [Bal]

Each voter grades each candidate according to some pre-specified finite grading scale expressed in verbal terms. For each candidate one computes his median grade. Among the candidates with the highest median grade, a linear approximation scheme (described in [START_REF] Balinski | A theory of measuring, electing, and ranking[END_REF] is used in order to choose the elected candidate. See Basset and Persky (1999), Gerlein and Lepelley (2003), [START_REF] Felsenthal | The Majority Judgment Voting Procedure: A Critical Evaluation[END_REF], [START_REF] Laslier | On choosing the alternative with the best median evaluation[END_REF]. Other names for this procedure or its variants: "Robust voting", "Best median".

Simpson [Sim]

Each voter submits a ranking of the candidates. The pair-wise vote matrix is computed. Then the chosen candidate is the one against which the smallest majority (in favor of another candidate) can be gathered. See [START_REF] Simpson | On defining areas of voter choice[END_REF]. Other names: "Minimax procedure", "Simpson-Kramer rule".

Borda [Bor]

Each voter submits a ranking of the candidates. For K candidates, each one receives K -1 points each time he is ranked first, K -2 points each time he is ranked second, etc. The elected candidate is the one who receives the largest number of points.

Black [Bla]

Choose the Condorcet winner if it exists and the Borda winner if not. Suggested by [START_REF] Black | The Theory of Committees and Elections[END_REF].

Nanson [Nan]

Each voter submits a ranking of the candidates. The Borda score is computed. Candidates with Borda score equal to or below the average are eliminated. Then a new Borda count is computed, on the reduced profile and the process is iterated. This procedure is Condorcet-consistent. See [START_REF] Nanson | Methods of elections[END_REF].

Range Voting [RV]

Each voter gives to each candidate as many points as she wishes between zero and, say, 10 points. The elected candidate is the one who receives the largest number of points. Range Voting is not often considered in the voting rule literature since, from the theoretical point of view, it is essentially plain utilitarianism. See Arrow, Sen and Suzumura (2002), [START_REF] Dhillon | Relative utilitarianism[END_REF], [START_REF] Baujard | Framed-field experiments on approval voting in the political context[END_REF] or the rangevoting.org web site. Other names for this procedure or its variants: "Utilitarianism", "Point voting" and in French: "vote par note", which just means "voting by grading."

Top Cycle [TC]

Each voter submits a ranking of the candidates. The majority tournament is computed. The Top-Cycle is the smallest set of candidates such that all candidates in this set beat all candidates outside this set. This Condorcet-consistent rule does not specify how ties (which occur when there is no Condorcet winner) are broken. See [START_REF] Schwartz | Rationality and the myth of maximum[END_REF], [START_REF] Laslier | Tournament Solutions and Majority Voting[END_REF].

Uncovered set [UC]

Each voter submits a ranking of the candidates. The majority tournament is computed. A candidate a belongs to the Uncovered set if and only if, for any other candidate b, either a beats b or a beats some c who beats b. This Condorcet-consistent rule does not specify how ties (which occur when there is no Condorcet winner) are broken. See [START_REF] Miller | A new solution for tournaments and majority voting[END_REF], [START_REF] Mckelvey | Covering, dominance, and institution-free properties of social choice[END_REF], [START_REF] Laslier | Tournament Solutions and Majority Voting[END_REF]. Other name (in the graph-theory literature): "Kings procedure". called the total variance, and compare this sum to the sum of squares of the distances between the corresponding points: ∑ c,c (φ (c)φ (c )) 2 , called the explained variance. The best representation with d dimensions can be computed numerically using linear algebra. The quality of the representation is measured by the ratio between explained and total variance. This technique was used for Approval Voting data by Laslier and Van der Straeten (2004) and by [START_REF] Laslier | Spatial approval voting[END_REF].

Of course the quality of the representation can only increase with the number of dimensions. In the text I show a 3D representation that explains about 90% of the the variance. In order to check whether this figure should be considered as large, I replicated the same computation on randomly generated data. Recall that, with the real data the explained percentages are, respectively 39, 66 and 90 for 1, 2 and 3 dimensions.

In a first test, suppose that each voter approves of each candidate independently with a probability p that corresponds to the average approval rate (here: p = 78/(15 * 22) .236). Running 10.000 simulations I find that the observed figures 39%, 66%, 90%) are respectively attained with probability .016, .005 and .0005. It is thus clear that our data set has much more structure than a totally random one, in which all candidates are alike, up to random fluctuations.

In a second test, suppose that we set the expected number of approval votes received by each candidate c to its actual value. So suppose that each voter independently approves of each candidate c with a probability p(c) equal to the actual approving percentage of this candidate. For instance for the candidate Approval Voting, p(App) = 15/22 .6818. We thus keep trace that some candidates are good and some are not, but we lose the correlation among candidates. In that case, I find that that the observed figures (39%, 66%, 90%) are respectively attained with probability .07, .07 and .03. Again one can conclude from this statistical test that it is not by chance that the real data set provides such large figures.

Fig. 2

 2 Fig. 1 Axes 1 and 2

  Range (100) > Approval (99) > Kramer-Simpson (85) > Coombs (84) > Kemeny (83) > Copeland (82) > Nanson (81) > Black (80) > Borda (50) > Fishburn (21) > UncoveredSet (20) > 2-roundMajority (18) > AlternativeVote (17) > UntrappedSet (16) > TopCycle (15) > Leximin (10) > Majority Judgment (1) > Plurality (0)

Table 1

 1 Number of approved candidates

Table 2

 2 Approval scoresFocus The focus of candidate c is the sum over all candidates k of the fraction of c-voters who also approved k.

	The candidate "present at date

Table 5

 5 Association matrix App Alt Cop Kem 2R Coo Sim Bal Bor Bla RV Nan Lex TC UC

	App 1	.7 .78 .5 .5 .5 .8 1	.75 1	1 1	1	1
	Alt .47 1	.22 .38 .83 .67 .6 .6 .25 1	.5 .5 1	1
	Cop .47 .2 1	.5 .17 .33 .6 .8 .50 .33 0 1	0	0
	Kem .27 .3 .44 1
									.33 0 1	0	0
	Bla .20 .3 .11 .12 .33 .17 .4 .2 .25 1	0 .5 1	1
	RV .13 .1 0	0	0 .17 0	.2 0	0	1 0	0	0
	Nan .13 .1 .22 .12 .17 .17 .4 .2 .5 .33 0 1	0	0
	Lex .07 .1 0	0	.17 0	0	0	0	.33 0 0	1	0
	TC .07 .1 0	.12 0 0	.2 0	0	.33 0 0	0	1
	UC .07 0	.11 .12 0 0	.2 0	.25 0	0 .5 0	0

.17 .5 .6 .2 .25 .33 0 .5 0 1 2R .2 .5 .11 .12 1 .5 .2 .2 .5 .67 0 .5 1 0 Coo .2 .4 .22 .38 .5 1 .2 .4 .25 .33 .5 .5 0 0 Sim .27 .3 .33 .38 .17 .17 1 .4 .50 .67 0 1 0 1 Bal .33 .3 .44 .12 .17 .33 .4 1 .25 .33 .5 .5 0 0 Bor .20 .1 .22 .12 .33 .17 .4 .2 1

Table 6

 6 Conditional association matrix

  Figures 1 and 2 are side views of this representation. Approval Voting is in the center. The points on the right are rules which are important in the social choice literature: Uncovered set, Copeland, Nanson, Kemeny, Simpson, even if they are not very practical. Borda is in this group, close to Nanson. The points on the left contain three practical solutions to the voting problem: Two-round majority, the Alternative Vote, and Black. Leximin is not far from this group. Coombs and Majority Judgement are close one to the other, with Range Voting not far. The Top-cycle is isolated.This structure reflects the vote profile since by definition, two voting rules are represented close one to the other when the same voters approved both.

My guess, based on the theoretical analysis of strategic voting under Approval Voting, is that the result would not be different.

The existence of several Condorcet winners simultaneously is a rare phenomenon.

No randomization scheme was considered. In particular the optimal solutions to the Condorcet paradox studied by Laffond, Laslier and LeBreton (1993) and[START_REF] Dutta | Comparison functions and choice correspondences[END_REF] were not on the list of voting procedures.

See the cloning-consistency condition[START_REF] Tideman | Independence of clones as a criterion for voting rules[END_REF]) and the composition-consistency property[START_REF] Laffond | Composition-consistent tournament solutions and social choice functions[END_REF].

One voter wrote on his/her ballot "Approval Voting with a runoff." This procedure was not on the list. This ballot was counted as an approbation of Approval voting.

See Appendix 3 for more details.

Thanks to Dan Felsenthal for pointing to me details of this definition.

Fishburn

This choice correspondence is a variant of the Uncovered set which is useful when the majority relation contains ties (exactly as many voters prefer a to b than b to a). See Aleskerov and Kurbanov (1999).

Untrapped set

This choice correspondence defined by Duggan (2007) is a variant of the Top-Cycle which is useful when the majority relation contains ties (exactly as many voters prefer a to b than b to a).

Plurality

Each voter votes for one candidate. The candidate with the most votes is elected. This is the most common voting rule in the Anglo-saxon world and the literature is very large. Other name: First Past the Post.

W. Zwicker

When I suggested we vote on voting rules and use Approval Voting, I thought the proposal could not pass -we'd surely split over the use of Approval Voting. At the time, however, our "rump session" discussion was stuck and it seemed that a conversational grenade might do more good than harm. I was very surprised that no one objected; some, as one might expect, were enthusiastic. Then I realized the exercise might be constructive if we could collectively endorse the principle that plurality rule was terrible... despite the stated goals of our workshop, I'd never thought it likely that we'd reach even a loose consensus on a single alternative. My own ballot approved a large number of rules, for two reasons: I doubt that the current state-ofthe-art allows us confidently to select a small number of best rules, and my genuine indecisiveness was consistent with the best strategy for making plurality look bad. In terms of my specific approvals, it seems like false comfort to rely on any single absolute principle as a guide, when every choice of a voting rule entails trade-offs along many dimensions, about which our understanding is limited. For example, I feel the draw of Condorcet's principle but reject it as an absolute, in part because some recent results suggest trade-offs between that principle and any reasonable degree of decisiveness. I've come to view decisiveness as an under-valued trait -very important, though not decisively so of course. I did approve some Condorcet extensions, but not top-cycle, because of its striking indecisiveness. Mathematically, Kemeny is beautiful whereas Black is plug-ugly, but I swallowed hard, approved Black, and disapproved Kemeny (because Kemeny winner are rankings, not individual candidates, and I can imagine what would happen the first time some real world election yielded a tie among several rankings).

Appendix 2: 18 voting rules

In what follows, the "majority tournament" is the binary relation among candidates: "More than half of the voters prefer a to b". In that case we say that a beats b (according to pair-wise majority rule).

Approval voting [App]

Each voter approves as many candidates as she wishes. The candidate with the most approval is elected. See [START_REF] Brams | Approval Voting[END_REF], Laslier and Sanver (2010).

Appendix 3: Statistical significance of the 3D representation

The method for spatial representation of data sets is derived from multivariate factor analysis. Given is a symmetric matrix of positive numbers, intended to measure the distances between the items, say dist(c, c ). If each item c is represented by a point φ (c) in the Euclidean space of dimension d one can compute the sum of the squares of the distances between the items: ∑ c,c dist 2 (c, c ),