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Talk:Judicial functions of the House of Lords

Lord Chancellor and Lord High Steward
"Normally, the Lord Chancellor presides at the trial. If, however, a peer is tried for high treason, the Lord High Steward presides." According to our article Lord High Steward, if a peer was tried, a Lord High Steward was appointed to preside over the trial. This was usually the Lord Chancellor, the usual president of the House of Lords. J S Ayer (talk) 13:26, 31 August 2011 (UTC)

O'Connell
So, current statement: "A panel of Law Lords—the Lord Chancellor, three former Lord Chancellors, a former Lord Chancellor of Ireland and a former Lord Chief Justice" were involved in reviewing O'Connell's case.

Okay, so the current Lord Chancellor in 1844 was Lord Lyndhurst; the former Lord Chancellor of Ireland was either Lord Plunket or Lord Campbell (it'd be nice to know which); two of the former Lord Chancellors must have been Lord Brougham and Lord Cottenham. But I can't figure out who the third former lord chancellor or the former Lord Chief Justice might have been. The other most recent Lord Chancellors were Lord Erskine and Lord Eldon, both of whom had been dead for some time by 1844. So far as I can tell, there were no living former Lord Chief Justices, either - both Lord Ellenborough and Lord Tenterden were long dead. Am I missing something? john k (talk) 15:31, 27 April 2013 (UTC)

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Groundwater

Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidated deposit is called an aquifer when it can yield a usable quantity of water. The depth at which soil pore spaces or fractures and voids in rock become completely saturated with water is called the water table. Groundwater is recharged from the surface; it may discharge from the surface naturally at springs and seeps, and can form oases or wetlands. Groundwater is also often withdrawn for agricultural, municipal, and industrial use by constructing and operating extraction wells. The study of the distribution and movement of groundwater is hydrogeology, also called groundwater hydrology.

Typically, groundwater is thought of as water flowing through shallow aquifers, but, in the technical sense, it can also contain soil moisture, permafrost (frozen soil), immobile water in very low permeability bedrock, and deep geothermal or oil formation water. Groundwater is hypothesized to provide lubrication that can possibly influence the movement of faults. It is likely that much of Earth's subsurface contains some water, which may be mixed with other fluids in some instances.

Groundwater is often cheaper, more convenient and less vulnerable to pollution than surface water. Therefore, it is commonly used for public water supplies. For example, groundwater provides the largest source of usable water storage in the United States, and California annually withdraws the largest amount of groundwater of all the states. Underground reservoirs contain far more water than the capacity of all surface reservoirs and lakes in the US, including the Great Lakes. Many municipal water supplies are derived solely from groundwater. Over 2 billion people rely on it as their primary water source worldwide.

Human use of groundwater causes environmental problems. For example, polluted groundwater is less visible and more difficult to clean up than pollution in rivers and lakes. Groundwater pollution most often results from improper disposal of wastes on land. Major sources include industrial and household chemicals and garbage landfills, excessive fertilizers and pesticides used in agriculture, industrial waste lagoons, tailings and process wastewater from mines, industrial fracking, oil field brine pits, leaking underground oil storage tanks and pipelines, sewage sludge and septic systems. Additionally, groundwater is susceptible to saltwater intrusion in coastal areas and can cause land subsidence when extracted unsustainably, leading to sinking cities (like Bangkok) and loss in elevation (such as the multiple meters lost in the Central Valley of California). These issues are made more complicated by sea level rise and other effects of climate change, particularly those on the water cycle. Earth's axial tilt has shifted 31 inches because of human groundwater pumping.

Definition
Groundwater is fresh water located in the subsurface pore space of soil and rocks. It is also water that is flowing within aquifers below the water table. Sometimes it is useful to make a distinction between groundwater that is closely associated with surface water, and deep groundwater in an aquifer (called "fossil water" if it infiltrated into the ground millennia ago ).

Role in the water cycle

Groundwater can be thought of in the same terms as surface water: inputs, outputs and storage. The natural input to groundwater is seepage from surface water. The natural outputs from groundwater are springs and seepage to the oceans. Due to its slow rate of turnover, groundwater storage is generally much larger (in volume) compared to inputs than it is for surface water. This difference makes it easy for humans to use groundwater unsustainably for a long time without severe consequences. Nevertheless, over the long term the average rate of seepage above a groundwater source is the upper bound for average consumption of water from that source.

Groundwater is naturally replenished by surface water from precipitation, streams, and rivers when this recharge reaches the water table.

Groundwater can be a long-term 'reservoir' of the natural water cycle (with residence times from days to millennia), as opposed to short-term water reservoirs like the atmosphere and fresh surface water (which have residence times from minutes to years). Deep groundwater (which is quite distant from the surface recharge) can take a very long time to complete its natural cycle.

The Great Artesian Basin in central and eastern Australia is one of the largest confined aquifer systems in the world, extending for almost 2 million km2. By analysing the trace elements in water sourced from deep underground, hydrogeologists have been able to determine that water extracted from these aquifers can be more than 1 million years old.

By comparing the age of groundwater obtained from different parts of the Great Artesian Basin, hydrogeologists have found it increases in age across the basin. Where water recharges the aquifers along the Eastern Divide, ages are young. As groundwater flows westward across the continent, it increases in age, with the oldest groundwater occurring in the western parts. This means that in order to have travelled almost 1000 km from the source of recharge in 1 million years, the groundwater flowing through the Great Artesian Basin travels at an average rate of about 1 metre per year.

Temperature
The high specific heat capacity of water and the insulating effect of soil and rock can mitigate the effects of climate and maintain groundwater at a relatively steady temperature. In some places where groundwater temperatures are maintained by this effect at about 10 °C, groundwater can be used for controlling the temperature inside structures at the surface. For example, during hot weather relatively cool groundwater can be pumped through radiators in a home and then returned to the ground in another well. During cold seasons, because it is relatively warm, the water can be used in the same way as a source of heat for heat pumps that is much more efficient than using air.

Availability
Groundwater makes up about thirty percent of the world's fresh water supply, which is about 0.76% of the entire world's water, including oceans and permanent ice. About 99% of the world's liquid fresh water is groundwater. Global groundwater storage is roughly equal to the total amount of freshwater stored in the snow and ice pack, including the north and south poles. This makes it an important resource that can act as a natural storage that can buffer against shortages of surface water, as in during times of drought.

The volume of groundwater in an aquifer can be estimated by measuring water levels in local wells and by examining geologic records from well-drilling to determine the extent, depth and thickness of water-bearing sediments and rocks. Before an investment is made in production wells, test wells may be drilled to measure the depths at which water is encountered and collect samples of soils, rock and water for laboratory analyses. Pumping tests can be performed in test wells to determine flow characteristics of the aquifer.

The characteristics of aquifers vary with the geology and structure of the substrate and topography in which they occur. In general, the more productive aquifers occur in sedimentary geologic formations. By comparison, weathered and fractured crystalline rocks yield smaller quantities of groundwater in many environments. Unconsolidated to poorly cemented alluvial materials that have accumulated as valley-filling sediments in major river valleys and geologically subsiding structural basins are included among the most productive sources of groundwater.

Fluid flows can be altered in different lithological settings by brittle deformation of rocks in fault zones; the mechanisms by which this occurs are the subject of fault zone hydrogeology.

Uses by humans
Reliance on groundwater will only increase, mainly due to growing water demand by all sectors combined with increasing variation in rainfall patterns.

Quantities
Groundwater is the most accessed source of freshwater around the world, including as drinking water, irrigation, and manufacturing. Groundwater accounts for about half of the world's drinking water, 40% of its irrigation water, and a third of water for industrial purposes.

Another estimate stated that globally groundwater accounts for about one third of all water withdrawals, and surface water for the other two thirds. Groundwater provides drinking water to at least 50% of the global population. About 2.5 billion people depend solely on groundwater resources to satisfy their basic daily water needs.

A similar estimate was published in 2021 which stated that "groundwater is estimated to supply between a quarter and a third of the world's annual freshwater withdrawals to meet agricultural, industrial and domestic demands."

Global freshwater withdrawal was probably around 600 km3 per year in 1900 and increased to 3,880 km3 per year in 2017. The rate of increase was especially high (around 3% per year) during the period 1950–1980, partly due to a higher population growth rate, and partly to rapidly increasing groundwater development, particularly for irrigation. The rate of increase is (as per 2022) approximately 1% per year, in tune with the current population growth rate.

Global groundwater depletion has been calculated to be between 100 and 300 km3 per year. This depletion is mainly caused by "expansion of irrigated agriculture in drylands".

The Asia-Pacific region is the largest groundwater abstractor in the world, containing seven out of the ten countries that extract most groundwater (Bangladesh, China, India, Indonesia, Iran, Pakistan and Turkey). These countries alone account for roughly 60% of the world's total groundwater withdrawal.

Drinking water quality aspects
Groundwater may or may not be a safe water source. In fact, there is considerable uncertainty with groundwater in different hydrogeologic contexts: the widespread presence of contaminants such as arsenic, fluoride and salinity can reduce the suitability of groundwater as a drinking water source. Arsenic and fluoride have been considered as priority contaminants at a global level, although priority chemicals will vary by country.

There is a lot of heterogeneity of hydrogeologic properties. For this reason, salinity of groundwater is often highly variable over space. This contributes to highly variable groundwater security risks even within a specific region. Salinity in groundwater makes the water unpalatable and unusable and often occurs in coastal areas, for example in Bangladesh and East and West Africa.

Water supply for municipal and industrial uses
Municipal and industrial water supplies are provided through large wells. Multiple wells for one water supply source are termed "wellfields", which may withdraw water from confined or unconfined aquifers. Using groundwater from deep, confined aquifers provides more protection from surface water contamination. Some wells, termed "collector wells", are specifically designed to induce infiltration of surface (usually river) water.

Aquifers that provide sustainable fresh groundwater to urban areas and for agricultural irrigation are typically close to the ground surface (within a couple of hundred metres) and have some recharge by fresh water. This recharge is typically from rivers or meteoric water (precipitation) that percolates into the aquifer through overlying unsaturated materials.

Irrigation
In general, the irrigation of 20% of farming land (with various types of water sources) accounts for the production of 40% of food production. Irrigation techniques across the globe includes canals redirecting surface water, groundwater pumping, and diverting water from dams. Aquifers are critically important in agriculture. Deep aquifers in arid areas have long been water sources for irrigation. A majority of extracted groundwater, 70%, is used for agricultural purposes.

In India, 65% of the irrigation is from groundwater and about 90% of extracted groundwater is used for irrigation.

Occasionally, sedimentary or "fossil" aquifers are used to provide irrigation and drinking water to urban areas. In Libya, for example, Muammar Gaddafi's Great Manmade River project has pumped large amounts of groundwater from aquifers beneath the Sahara to populous areas near the coast. Though this has saved Libya money over the alternative, seawater desalination, the aquifers are likely to run dry in 60 to 100 years.

Challenges
First, flood mitigation schemes, intended to protect infrastructure built on floodplains, have had the unintended consequence of reducing aquifer recharge associated with natural flooding. Second, prolonged depletion of groundwater in extensive aquifers can result in land subsidence, with associated infrastructure damage – as well as, third, saline intrusion. Fourth, draining acid sulphate soils, often found in low-lying coastal plains, can result in acidification and pollution of formerly freshwater and estuarine streams.

Overdraft
Groundwater is a highly useful and often abundant resource. Most land areas on Earth have some form of aquifer underlying them, sometimes at significant depths. In some cases, these aquifers are rapidly being depleted by the human population. Such over-use, over-abstraction or overdraft can cause major problems to human users and to the environment. The most evident problem (as far as human groundwater use is concerned) is a lowering of the water table beyond the reach of existing wells. As a consequence, wells must be drilled deeper to reach the groundwater; in some places (e.g., California, Texas, and India) the water table has dropped hundreds of feet because of extensive well pumping. The GRACE satellites have collected data that demonstrates 21 of Earth's 37 major aquifers are undergoing depletion. In the Punjab region of India, for example, groundwater levels have dropped 10 meters since 1979, and the rate of depletion is accelerating. A lowered water table may, in turn, cause other problems such as groundwater-related subsidence and saltwater intrusion.

Another cause for concern is that groundwater drawdown from over-allocated aquifers has the potential to cause severe damage to both terrestrial and aquatic ecosystems – in some cases very conspicuously but in others quite imperceptibly because of the extended period over which the damage occurs. The importance of groundwater to ecosystems is often overlooked, even by freshwater biologists and ecologists. Groundwaters sustain rivers, wetlands, and lakes, as well as subterranean ecosystems within karst or alluvial aquifers.

Not all ecosystems need groundwater, of course. Some terrestrial ecosystems – for example, those of the open deserts and similar arid environments – exist on irregular rainfall and the moisture it delivers to the soil, supplemented by moisture in the air. While there are other terrestrial ecosystems in more hospitable environments where groundwater plays no central role, groundwater is in fact fundamental to many of the world's major ecosystems. Water flows between groundwaters and surface waters. Most rivers, lakes, and wetlands are fed by, and (at other places or times) feed groundwater, to varying degrees. Groundwater feeds soil moisture through percolation, and many terrestrial vegetation communities depend directly on either groundwater or the percolated soil moisture above the aquifer for at least part of each year. Hyporheic zones (the mixing zone of streamwater and groundwater) and riparian zones are examples of ecotones largely or totally dependent on groundwater.

A 2021 study found that of ~39 million investigated groundwater wells 6-20% are at high risk of running dry if local groundwater levels decline by a few meters, or – as with many areas and possibly more than half of major aquifers – continue to decline.

Fresh-water aquifers, especially those with limited recharge by snow or rain, also known as meteoric water, can be over-exploited and depending on the local hydrogeology, may draw in non-potable water or saltwater intrusion from hydraulically connected aquifers or surface water bodies. This can be a serious problem, especially in coastal areas and other areas where aquifer pumping is excessive.

Subsidence
Subsidence occurs when too much water is pumped out from underground, deflating the space below the above-surface, and thus causing the ground to collapse. The result can look like craters on plots of land. This occurs because, in its natural equilibrium state, the hydraulic pressure of groundwater in the pore spaces of the aquifer and the aquitard supports some of the weight of the overlying sediments. When groundwater is removed from aquifers by excessive pumping, pore pressures in the aquifer drop and compression of the aquifer may occur. This compression may be partially recoverable if pressures rebound, but much of it is not. When the aquifer gets compressed, it may cause land subsidence, a drop in the ground surface.

In unconsolidated aquifers, groundwater is produced from pore spaces between particles of gravel, sand, and silt. If the aquifer is confined by low-permeability layers, the reduced water pressure in the sand and gravel causes slow drainage of water from the adjoining confining layers. If these confining layers are composed of compressible silt or clay, the loss of water to the aquifer reduces the water pressure in the confining layer, causing it to compress from the weight of overlying geologic materials. In severe cases, this compression can be observed on the ground surface as subsidence. Unfortunately, much of the subsidence from groundwater extraction is permanent (elastic rebound is small). Thus, the subsidence is not only permanent, but the compressed aquifer has a permanently reduced capacity to hold water.

The city of New Orleans, Louisiana is actually below sea level today, and its subsidence is partly caused by removal of groundwater from the various aquifer/aquitard systems beneath it. In the first half of the 20th century, the San Joaquin Valley experienced significant subsidence, in some places up to 8.5 m due to groundwater removal. Cities on river deltas, including Venice in Italy, and Bangkok in Thailand, have experienced surface subsidence; Mexico City, built on a former lake bed, has experienced rates of subsidence of up to 40 cm per year.

For coastal cities, subsidence can increase the risk of other environmental issues, such as sea level rise. For example, Bangkok is expected to have 5.138 million people exposed to coastal flooding by 2070 because of these combining factors.

Groundwater becoming saline due to evaporation
If the surface water source is also subject to substantial evaporation, a groundwater source may become saline. This situation can occur naturally under endorheic bodies of water, or artificially under irrigated farmland. In coastal areas, human use of a groundwater source may cause the direction of seepage to ocean to reverse which can also cause soil salinization.

As water moves through the landscape, it collects soluble salts, mainly sodium chloride. Where such water enters the atmosphere through evapotranspiration, these salts are left behind. In irrigation districts, poor drainage of soils and surface aquifers can result in water tables' coming to the surface in low-lying areas. Major land degradation problems of soil salinity and waterlogging result, combined with increasing levels of salt in surface waters. As a consequence, major damage has occurred to local economies and environments.

Aquifers in surface irrigated areas in semi-arid zones with reuse of the unavoidable irrigation water losses percolating down into the underground by supplemental irrigation from wells run the risk of salination.

Surface irrigation water normally contains salts in the order of $0.5 g/L$ or more and the annual irrigation requirement is in the order of $10,000 m3/ha$ or more so the annual import of salt is in the order of $5,000 kg/ha$ or more.

Under the influence of continuous evaporation, the salt concentration of the aquifer water may increase continually and eventually cause an environmental problem.

For salinity control in such a case, annually an amount of drainage water is to be discharged from the aquifer by means of a subsurface drainage system and disposed of through a safe outlet. The drainage system may be horizontal (i.e. using pipes, tile drains or ditches) or vertical (drainage by wells). To estimate the drainage requirement, the use of a groundwater model with an agro-hydro-salinity component may be instrumental, e.g. SahysMod.

Seawater intrusion
Aquifers near the coast have a lens of freshwater near the surface and denser seawater under freshwater. Seawater penetrates the aquifer diffusing in from the ocean and is denser than freshwater. For porous (i.e., sandy) aquifers near the coast, the thickness of freshwater atop saltwater is about 40 ft for every 1 ft of freshwater head above sea level. This relationship is called the Ghyben-Herzberg equation. If too much groundwater is pumped near the coast, salt-water may intrude into freshwater aquifers causing contamination of potable freshwater supplies. Many coastal aquifers, such as the Biscayne Aquifer near Miami and the New Jersey Coastal Plain aquifer, have problems with saltwater intrusion as a result of overpumping and sea level rise.

Seawater intrusion is the flow or presence of seawater into coastal aquifers; it is a case of saltwater intrusion. It is a natural phenomenon but can also be caused or worsened by anthropogenic factors, such as sea level rise due to climate change. In the case of homogeneous aquifers, seawater intrusion forms a saline wedge below a transition zone to fresh groundwater, flowing seaward on the top. These changes can have other effects on the land above the groundwater. For example, coastal groundwater in California would rise in many aquifers, increasing risks of flooding and runoff challenges.

Sea level rise causes the mixing of sea water into the coastal groundwater, rendering it unusable once it amounts to more than 2-3% of the reservoir. Along an estimated 15% of the US coastline, the majority of local groundwater levels are already below the sea level.

Climate change

The impacts of climate change on groundwater may be greatest through its indirect effects on irrigation water demand via increased evapotranspiration. There is an observed declined in groundwater storage in many parts of the world. This is due to more groundwater being used for irrigation activities in agriculture, particularly in drylands. Some of this increase in irrigation can be due to water scarcity issues made worse by effects of climate change on the water cycle. Direct redistribution of water by human activities amounting to ~24,000 km3 per year is about double the global groundwater recharge each year.

Climate change causes changes to the water cycle which in turn affect groundwater in several ways: There can be a decline in groundwater storage, and reduction in groundwater recharge and water quality deterioration due to extreme weather events. In the tropics intense precipitation and flooding events appear to lead to more groundwater recharge.

However, the exact impacts of climate change on groundwater are still under investigation. This is because scientific data derived from groundwater monitoring is still missing, such as changes in space and time, abstraction data and "numerical representations of groundwater recharge processes".

Effects of climate change could have different impacts on groundwater storage: The expected more intense (but fewer) major rainfall events could lead to increased groundwater recharge in many environments. But more intense drought periods could result in soil drying-out and compaction which would reduce infiltration to groundwater.

For the higher altitudes regions, the reduced duration and amount of snow may lead to reduced recharge of groundwater in spring. The impacts of receding alpine glaciers on groundwater systems are not well understood.

Global sea level rise due to climate change has induced seawater intrusion into coastal aquifers around the world, particularly in low-lying areas and small islands. However, groundwater abstraction is usually the main reason for seawater intrusion, rather than sea level rise (see in section on seawater intrusion). Seawater intrusion threatens coastal ecosystems and livelihood resilience. Bangladesh is a vulnerable country for this issue, and mangrove forest of Sundarbans is a vulnerable ecosystem.

Groundwater pollution may also increase indirectly due to climate change: More frequent and intense storms can pollute groundwater by mobilizing contaminants, for example fertilizers, wastewater or human excreta from pit latrines. Droughts reduce river dilution capacities and groundwater levels, increasing the risk of groundwater contamination.

Aquifer systems that are vulnerable to climate change include the following examples (the first four are largely independent of human withdrawals, unlike examples 5 to 8 where the intensity of human groundwater withdrawals plays a key role in amplifying vulnerability to climate change):
 * 1) low-relief coastal and deltaic aquifer systems,
 * 2) aquifer systems in continental northern latitudes or alpine and polar regions
 * 3) aquifers in rapidly expanding low-income cities and large displaced and informal communities
 * 4) shallow alluvial aquifers underlying seasonal rivers in drylands,
 * 5) intensively pumped aquifer systems for groundwater-fed irrigation in drylands
 * 6) intensively pumped aquifers for dryland cities
 * 7) intensively pumped coastal aquifers
 * 8) low-storage/low-recharge aquifer systems in drylands

Climate change adaptation
Using more groundwater, particularly in Sub-Saharan Africa, is seen as a method for climate change adaptation in the case that climate change causes more intense or frequent droughts.

Groundwater-based adaptations to climate change exploit distributed groundwater storage and the capacity of aquifer systems to store seasonal or episodic water surpluses. They incur substantially lower evaporative losses than conventional infrastructure, such as surface dams. For example, in tropical Africa, pumping water from groundwater storage can help to improve the climate resilience of water and food supplies.

Climate change mitigation
The development of geothermal energy, a sustainable energy source, plays an important role in reducing CO2 emissions and thus mitigating climate change. Groundwater is an agent in the storage, movement, and extraction of geothermal energy.

In pioneering nations, such as the Netherlands and Sweden, the ground/groundwater is increasingly seen as just one component (a seasonal source, sink or thermal 'buffer') in district heating and cooling networks.

Deep aquifers can also be used for carbon capture and sequestration, the process of storing carbon to curb accumulation of carbon dioxide in the atmosphere.

Groundwater governance
Groundwater governance processes enable groundwater management, planning and policy implementation. It takes place at multiple scales and geographic levels, including regional and transboundary scales.

Groundwater management is action-oriented, focusing on practical implementation activities and day-to-day operations. Because groundwater is often perceived as a private resource (that is, closely connected to land ownership, and in some jurisdictions treated as privately owned), regulation and top–down governance and management are difficult. Governments need to fully assume their role as resource custodians in view of the common-good aspects of groundwater.

Domestic laws and regulations regulate access to groundwater as well as human activities that impact the quality of groundwater. Legal frameworks also need to include protection of discharge and recharge zones and of the area surrounding water supply wells, as well as sustainable yield norms and abstraction controls, and conjunctive use regulations. In some jurisdictions, groundwater is regulated in conjunction with surface water, including rivers.

By country
Groundwater is an important water resource for the supply of drinking water, especially in arid countries.

The Arab region is one of the most water-scarce in the world and groundwater is the most relied-upon water source in at least 11 of the 22 Arab states. Over-extraction of groundwater in many parts of the region has led to groundwater table declines, especially in highly populated and agricultural areas.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Groundwater


text:
Talk:Monotonicity criterion

Tone
There's a "message board argument" tone to many sentences in the latter half of the article. "And not, as claimed by earlier versions of this wikipedia article, X" sounds childish. —Preceding unsigned comment added by 24.84.44.227 (talk) 13:53, 5 January 2011 (UTC)

Rights on the text
From the page:

 * Some parts of this article are derived from text at http://condorcet.org/emr/criteria.shtml

Some other pages have stated this, and said "used by permission". Can someone confirm that this use is by permission?

 * I did not seek explicit permission (though I may get around to sending a thank-you email). The linked page, at the very bottom, gives more than enough permission to re-distribute under the GFDL.  Indeed, the way that he phrased it there was no need to explicitly acknowledge his work, but I thought it would be good to do so, both to thank him, and because his site is a useful resource to link to.  DanKeshet 21:23 7 Jul 2003 (UTC)

Thanks! That's good news. -- Anon.

Don't confuse Condorcet criterion and monotonicity criterion
The comment that "several variants of the Condorcet method (including Cloneproof Schwartz Sequential Dropping and Maximize Affirmed Majorities) are monotonic" is misleading since there is no connection between the Condorcet criterion and the Monotonicity criterion. If you only want to say that the Condorcet criterion and the Monotonicity criterion are compatible, then it is sufficient to say that Cloneproof Schwartz Sequential Dropping and Maximize Affirmed Majorities are monotonic. -- Markus Schulze

 * Hmm, I don't think the para as it was asserts a connection between the Condorcet Criterion and MC. And though CSSD and MAM are different, they really are minor tweaks on the Condorcet Method and usually make the same decision, so it seems weird to write about them as if they were as different as Plurality and Borda. Is there any wording which mentions that these two are both Condorcet methods that would be acceptable to you? — ciphergoth 14:05, 2004 Nov 21 (UTC)

 * ciphergoth asked: "Is there any wording which mentions that these two are both Condorcet methods that would be acceptable to you?" No. The fact that CSSD and MAM satisfy the Monotonicity criterion must only be used to promote CSSD or MAM. But it must not be used to promote Condorcet methods in general or even a concrete Condorcet method that doesn't satisfy the Monotonicity criterion. -- Markus Schulze 21 Nov 2004

 * As ciphergoth, I fail to see how the sentence you talk about promotes Condorcet methods in general.--Chealer 03:36, 2004 Dec 10 (UTC)

Old edit war
I've reverted from a lot of edits by user:polytope. Polytope: you are wellcome to contribute to articles, but your material was really not appropriate, for at least the following reasons:

1) Wikipedia has a strict Neutral point of view policy which your discussion of the CVD definitely did not fit under. Please read that link for more information on how to construct NPOV pages.

2) It was very technical and frankly incomprehensible to me. You have to do a much better job of explaining your terms.

DanKeshet

Your decision is unfair, wrong, and unreasonable, so I intend to upload the page again, after at least 1/2 of a day or so. The spirit of fairness would be more present if I was the person editing the definitions. I expected details comments. Here are problems with your decision. My reasoning is more carefully done than yours. Note that the edit that you did is here: http://www.wikipedia.org/w/wiki.phtml?title=Monotonicity_criterion&diff=0&oldid=1126285

I assume you do not want to even read this, but do however wish to keep censoring with an indifference to how thoroughly an audience moves against you if publicity shows up. I find your decision to be unreasonable since it has been made without an obvious relationship to the facts or evidence. That is plain since except for the mention of the CVD, no other comment relates back to the text of the page. That refers to grounds #1 and #2. The decision to replace the page instead of editing it is found by me to be unreasonable in respect of ground #2 since it seems that you could have satisfied yourself by altering one or both of the words "[IRV is] promoted [in USA]" and "[the CVD] complains [about...]". Also you refused to provide reasoning by e-mail after I requested that. You had two grounds but the weights were missing so the significance of your failure to comprehend what I wrote is something that I now do not have. Any of my text could lucid and optimal though may misunderstand. You may refer to this for the theory of how to make decisions about me: .

Decisions should be accompanied with reasoning and reasoning is too inadequate to be present. I do very much suspect that you had an improper purpose for taking such a strong action over that article. I had not used a wikipedia before. I note that your initial friendliness fast became a lockout where I could not get fuller information about your reasoning. Your website is remarkable in carefully censoring out the idea of monontonicity (http://www.channel1.com/users/dkesh/green/voting/), yet it seems to aim to describe principles of preferential voting (and fails completely since none of those can be ported over to mathematics in my opinion). The fact censoring of censoring out that same anti-CVD topic is indicative of a consideration of an irrelevant factor (categorized under improper purpose). I requested (using private e-mail) a statement of the reasoning that was fuller and I never got any. Your argument was that I should write here at this page; that I now write to, and your grounds were "I don't read my e-mail very often." (you wrote on about 10-July-2003). That was a harassing decision. You intended to communicate only using private e-mail and you explained that since you receive and read your e-mail quite well (but a little slowly), then I must therefore avoid using e-mail (and use the wikipedia). That can not be followed and it is unreasonable. I was later? clear in stating that e-mail should be used and the wikipedia must not be. Why didn't you identify your error of telling me to use this wikipedia page ?. Ground #2 implied that you did not understand my mathematics page.

As I wrote at the Election Methods List, you made a mistake at your website indicating that you lack a knowledge of the principles of 2 candidate preferential methods. It was about "representation" in 2 candidate elections. I assume that you test is oppressive and harsh since setting an impossible hard standard for me: a requirement that you understand me when I write for the public with the plainest clarity I can achieve. I only have your word for it that you failed to understand my page. I reject the idea that you could not understand all of the page. Perhaps your 1st ground was oppressive since it told me to look at a policy document but it unreasonably failed to identify a problem or error in my text (or my behaviour) that would be guided to a better state by the policy document. I.e. you warned of how I could improve under policy without identifying what should get better. The CVD comment about non-neutrality with the CVD appeared to be untrue.

I accuse you of making an improperly discriminatory decision because you have worse reasoning and harsher actions for authors of monotonicity pages and me (so far). You maybe do not want your Green party to keep losing. Your decision was more adverse to the public interest than this: you made a lot of major changes. I have a diff program and it is convenient for me to undo only some of changes. Most of my complaint is about your lack of reasoning rather than the decision to erase the document and restore a worse one. Nowhere do you give an opinion on the difference between the documents. You decision was wrong to replace one document with another and have no consideration for the 2nd new document. The reasoning is required by me and there was consideration of you preferred version. I don't know why you prefer it. It is certainly less useful. The http://www.condorcet.org/ text does not reject the Alternative Vote (you wrongly opted for that), since mysteriously Mr B.C. confuses a preference with a candidate. That is unexplained. I have asked Mr B.C. to tell the Election Methods List and not enough time has passed. It seemed to be deliberate since the word "alternative" was used. So there is some improper purpose to the text you prefer (in addition to the possible improper purpose of not letting a monotonicity page harm Greens across USA over an unknown period of time). Greens should not be advanced by unthinkable definitions of others. That is a bit neutral on Greens and able to cause harm to members of the Election Methods List. Already Mr Eric Gorr has been confused by a definition from the condorcet.org website. My new version that I will upload is here, only in the box at the top: http://www.ijs.co.nz/irv-wrong-winners.htm The topic is mathematics and they are detailed. If you aer not, then you should quite withdraw. There is also a private dispute where I intend to comment adversely on your personal website but only fairly and accurately.

Craig Carey, New Zealand (no advice that I be anonymous) 'research at ijs.co.nz'. Wed 16-Jul-2003

Craig,

Responding to just a few of your points: I was perfectly reasonable in refusing to provide additional reasoning by e-mail; there is nothing that says I should spend my time responding to personal e-mails about wikipedia, especially not after you accused me of being "perverted" and "corrupt" and suggested I was taking bribes from user:RobLa. Also, judge my contributions on their merit, not on my supposed political views about voting systems. In any case, your assumptions about my views are inaccurate, sometimes wildly so.

On to your actual contribution. Here are my specific problems:

1) In your definition, you introduce the concept of a "weighted vote", without any explanation whatsoever of what that is. Also, your text is gramatically incorrect, ambiguous, and frankly incoherent.

2) The section titled "Centuries of fair voting ideals lost as use of IRV and STV spread" is chock full of hyperbole, and inappropriately placed. If you want to discuss the results of IRV, it would be better placed on the Instant-runoff voting page.  But don't be surprised if your section is heavily edited there, too.  In addition, you introduce the concept of "vote-negating" with barely any explanation.

3) The section titled "A human right to have a vote" is pure hyperbole, and belongs nowhere in an encyclopedia. If this were an actual tact that some people had taken, appealing for changes in voting systems to the UN under the "equal suffrage" clause, then we could as an encyclopedia, report that.  We can not engage in pure rhetoric, though.

4) The section titled "Parameterized 3 candidate method has IRV/AV be 33% outside of the fair region" has more unexplained jargon, as does the section "Dual of shadowing stays-losing polytope is a normal vector constraining polytope".

5) The section titled "Monotonicity is not best for theoreticians" is inappropriate for an encyclopedia, because we are here to report on how people study the monotonicity criterion, not argue that they should study it another way.

These are not all the problems I have with your text, but they are a start.

DanKeshet 13:51 16 Jul 2003 (UTC)

STV is never monotonic
I've removed text which stated that Single Transferable Vote can be non-monotonic depending on the methods used. No counting method (not even Meek's method) eliminates the non-monotonicity of STV - all counting methods reduce to IRV in single winner elections, and IRV is non-monotonic. Some counting methods, such as Meek's method, reduce the potential for tactical voting with STV, but they do not completely eliminate the non-monotonicity.

 * I amnot sure I agree with the removal. It is not enough to say that Meek's method cannot be montonic because 'STV' is never monotonic. That argument is circular. I will post a fuller answer at the STV talk page when I have researched it. Alan 09:46, 17 May 2005 (UTC).

 * When I added that text ("STV may or may not be monotonic, depending on the method used") I was actually thinking of Condorcet-STV, not Meek. Meek can be non-monotonic, though in real-world elections it is rare; see . Since Condorcet-STV doesn't actually tabulate vote transferral directly, it is not susceptible to the same analysis that indicts other STV systems; in some sense, Condorcet-STV is STV in effect, not in implementation. TreyHarris 15:25, 17 May 2005 (UTC)

 * Is there any proven statement that 'any' STV-method isn't monotonic? Like "any method that fulfills ... (which we call a 'STV-method') ... is not monotonic". Otherwise the most rigid statement should be "satisfaction of monotonicity criterion hasn't been proven for any known STV method". To write "all known STV methods are not monotonic" requires to show counter-examples for all of them. Please show me e.g. an example that Schulze STV is not monotonic. It reduces to the monotonic Schulze method in single winner elections, so any proposed counter-example must have at least two seats to be filled. Best, --Richard (talk) 11:52, 24 April 2014 (UTC)

If a voting system can be non-monotnic then it is fair to say that the system is a monotonic. Clearly any voting system is non-monotic sometimes. For example if there is unanamouse agreement about who the best candidate is. So when someone says that a system is non-monotonic they mean that there are circumstances where ranking someone higher can hurt them, given a certain pattern of votes. —Preceding unsigned comment added by 144.82.93.19 (talk) 09:47, 1 April 2011 (UTC)

 * "Clearly any voting system is non-monotic sometimes.". This is simply wrong. You might have written "Any voting system may be redesigned in some way (resulting in a different system), such that it becomes monotonic, or loses this property". Best, --Richard (talk) 11:33, 24 April 2014 (UTC)

Problem in the example?
In the example of a violation of the Monotonicity Criterion, it says that candidate C would be the Condorcet winner. However, it seems that there is no Condorcet winner in this case. In pairwise matchups C would beat A, A would beat B and B would beat C, meaning all three would be in the Smith Set. The winner would then depend on what form of Condorcet voting would take place. I would suggest solving this problem by either

1) Changing the second preference of A's voters to C (this will create 4 categories in the second election, but still result in a violation of monotonicity). Then in pairwise voting we would have C beats A and C beats B, meaning C is not the Condorcet winner.

2) Remark that there is no Condorcet winner and choose an appropriate resolution scheme, such as Minimax Condorcet, to choose a winner.

--Anon. 18:25:07, December 3, 2005 (UTC)

 * I cut the sentence completely. Why discuss what Condorcet methods will do instead of, say, Bucklin voting? It seems irrelevant to the article. KVenzke 17:46, 4 December 2005 (UTC)
 * Because condorcet methods pass the monotonicity criterion, that's why. You're right that Bucklin voting should be mentioned as well.  The article could use more examples, such as a sentence explaining why Bucklin passes too.  Scott Ritchie 18:35, 4 December 2005 (UTC)
 * Condorcet methods don't necessarily pass the monotonicity criterion. Consider Raynaud, Borda-Elimination (Nanson), or Smith//IRV. That's why it doesn't make sense to point out who the Condorcet winner is. KVenzke 04:16, 6 December 2005 (UTC)
 * Can you point out an example demonstrating that? It would be relevant to the article to show how they can fail. Scott Ritchie 00:10, 7 December 2005 (UTC)

Suppose that the method is Raynaud (wv), so that we repeatedly eliminate the candidate who has the most votes against him in a single pairwise contest. 36 abc 34 bca 30 cab C is eliminated and A wins. Now raise A on 5 bca ballots: 41 abc 29 bca 30 cab B is eliminated and C wins. I hope that's what you were looking for. KVenzke 22:58, 7 December 2005 (UTC)

Monotonic STV methods?
I have deleted the following sentence: "Most versions of the Single Transferable Vote which simplify to Instant Runoff when there is only one winner are not monotonic, however variants of STV such as CPO-STV and the Quota Borda system are." To the best of my knowledge, there is no STV method that has been proven to satisfy monotonicity. And the Quota Borda system has been proven to violate monotonicity. See example 3. Markus Schulze 09:22, 31 December 2005 (UTC)
 * Why not CPO-STV, or other methods that simplify to monotonic systems when there is one winner? Scott Ritchie 04:07, 2 January 2006 (UTC)
 * The Quota Borda system does simplify to a monotonic system when there is only one winner. Markus Schulze 09:50, 2 January 2006 (UTC)

Does The Example Fail To Fail The Monotonicity Criterion?
It is possible that I am missing something, but I am confused. It seems to me that the example given is not an example of a violation of the Monotonicity Criterion.

The Definition: "Douglas Woodall, calling the criterion mono-raise, defines it as: A candidate x should not be harmed [i.e., change from being a winner to a loser] if x is raised on some ballots without changing the orders of the other candidates." The Example: "1st Election 39 A,B 35 B,C 26 C,A C is eliminated, and A wins. 2nd Election 49 A,B 25 B,C 26 C,A B is eliminated, and C wins." The Example shows that A is the winner in the first election, but in the second election, A has a raised position yet loses, which seems to violate monotonicity. However, the Definition also states that candidate x should be harmed if x is raised without changing the orders of the other candidates. I guess I am confused because in the Example the orders of the candidates change. C is in 3rd place in the first election and changes to 2nd place in the second election. This, to me, is an example of a change in order of the candidates. If this is the case, then either another example is needed or the definition of the MC needs to be clarified. Otherwise, based on my current interpretation, I am not convinced that IRV, for instance, fails the MC.

"You are misunderstanding. 'without changing the orders of the other candidates' means that votes which ranked y > z still rank y > z. In the example we start with 39 A > B > C, 35 B > C > A, and 26 C > A > B for the first election.  We then take 10 of the B > C > A and change them to A > B > C, i.e. some voters increase their preference for A without changing the orders of the other candidates, all those votes still rank B > C.  After the change we have 49 A > B > C, 25 B > C > A, and 26 C > A > B, which causes A to lose the election and IRV to violatate the monotonicity criterion.  I'll be correcting the main article shortly.  206.104.161.170 (talk) 18:56, 20 June 2008 (UTC)"

Now, it could be interpretation is wrong and that the "changing the orders of the other candidates" means something else. It could mean a change in the secondary votes (for example, if the primary voters of C have secondary votes of A in the first election and change their secondary votes to B in the second election).

My point is that this article is confusing to someone who is not on expert on voting methods or voting system criterion. I am suggesting that this article could be clarified a little, but I do not consider myself knowledgeable enough to do so myself. Can someone either clarify the article or at least clarify this to me? Bryanmode 16:20, 6 November 2006 (UTC)

 * The reference to order changing is about the order of candidates on the ballot, not in some final ranking. Note that not all voting methods even produce a full ordered ranking -- the algorithm can simply halt when a winner (or N winners) are selected.  And no, basic IRV is definitely not monotonic.

 * Say you have an IRV election with three candidates ("A", "B", "C") and the votes are as follows:

 * 2 C > B > A
 * 6 A > B > C
 * 5 B > A > C
 * 4 C > B > A

 * The first group and fourth group look the same, but they're separated because we're going to explore what happens when the first group changes their vote.

 * First round: 6 votes for A, 5 for B, 6 for C. B is eliminated.
 * Second round: 11 votes for A, 6 votes for C. A wins.

 * Now, A does such a good job that the two voters in the first bloc decide they were wrong about A. So, in the next election, with all the same candidates, the votes are:

 * 2 A > C > B
 * 6 A > B > C
 * 5 B > A > C
 * 4 C > B > A

 * First round: 8 votes for A, 5 for B, 4 for C. C is eliminated.
 * Second round: 8 votes for A, 9 for B. B wins.

 * By ranking A higher, these two voters caused A to lose when A would've otherwise won.

 * Note that the relative order of the other candidates on the ballot in the first bloc (C > B) is unchanged. That's what was required by the condition you were discussing.

 * Ka-Ping Yee created an excellent graphical representation of IRV's monotonicity failure. Rmharman 06:40, 28 November 2006 (UTC)

Edit needed (by someone with more expertise than me)
The following sentence is incorrect:

''Tactical voting in this way presents an obvious risk if a voter's information about other ballots is wrong, however, and there is no evidence that voters actually pursue such counter-intuitive strategies in non-monotonic voting systems in real-world elections. ''

I don't have the time or indeed the expertise to edit the section properly, but somebody should. The second clause ("there is no evidence" etc.) has been quite plainly wrong since the German federal election of 2005, in which conservative voters in Dresden deliberately voted against their party of choice (the CDU) in order to maximize that party's number of seats in the federal parliament. This was possible due to Germany's voting system (mixed member proportional with overhang seats) and the fact that the vote in Dresden took place a week after the rest of the country due to the death of a candidate, enabling voters in Dresden to vote tactically in full knowledge of the results already achieved elsewhere. As a result of this, the German Constitutional Court ruled on July 3 2008 that the German voting system must be reformed to improve its monotonicity.

For more, see: (in English) or various German wikipedia articles such as   —Preceding unsigned comment added by 210.84.53.32 (talk) 04:19, 26 July 2009 (UTC)

Instant-runoff voting / Runoff voting (not monotonic)
The stated IRV example is not very realistic, because it contains a Condorcet cycle among the three Candidates in election one, with a very strong support for any of the three majorities in the cycle. I also criticize, that the example assumes a huge swing of the voters preferences. I suggest another example, without a Condorcet cycle, and just a small swing: Three candidates are running, a left, a right, and a center candidate. Hundred voters casting their ballots:

 * {| border="1" cellpadding="2"

 * Number of votes
 * 1st Preference
 * 2nd Preference
 * 28
 * Right
 * Center
 * 5
 * Right
 * Left
 * 35
 * Left
 * Center
 * 32
 * Center
 * }
 * 32
 * Center
 * }
 * }
 * }

The IRV-winner in that election would be Left, because Center gets eliminated first, and Left wins against Right according to the remaining preferences. But if the five voters, who voted 1st Left Right and 2nd Right  Left, switch their 1st and 2nd choice, then Right gets eliminated first, and Center wins against Left, so Left loses due to the new votes in favor of Left. -- Richard 13:45, 13 May 2011 (UTC)

-- Maybe I do not understand something, but nothing matches in the calculations in the article and in the talk page as well. "But if the five voters, who voted 1st Left and 2nd Right" - there are no such voters in the table given as the example. Also, in the article, given examples fail to prove the thesis they were brought for. Changing ranks from Right to Left entrenches the Left, not sets them down.

Robs777 (talk) 18:54, 11 October 2012 (UTC)

 * I corrected the error in the description of the example that's given here. In the article I used a different example. The two additional votes for Left in the article example (switching Right, Left, Center to Left, Right, Center) show a greater support for Left. That hurts Right in the first round, cause it no longer reaches the 2nd round. But Center, now entering 2nd round, beats Left. So the greater support for Left causes Left to lose, the result changes from Left winner, Right 2nd to Center winner, Left 2nd. Center is least prefered by the Left, Right, Center voters. Best, --Richard (talk) 10:53, 24 April 2014 (UTC)

Real-life monotonicity violations
Currently this section is misleading, a single election can't be used to show that a method violates monotonicity, therefore I propose to change this section as follows: When the ballots of a real election are released, it is fairly easy to proof, if it was possible
 * to defeat the winner by raising him on some of the ballots
 * to push a looser by lowering him on some of the ballots

This could be called a real-life monotonicity violation.

The ballots (or information allowing them to be reconstructed) are rarely released for instant runoff elections, which means there are few recorded monotonicity violations for real IRV elections. -- Richard 13:45, 13 May 2011 (UTC)

--- But any real-life election can be modelled in examples. I calculated figues given here as an examples and they do not confirm lack of monotonicity. I just want to understand how it really works. I seems that everybody talk about this but nobody can fetch any examples. Robs777 13:02, 15 October 2012 (UTC)
 * They do confirm, as they show that when X is winner, upranking X on some ballots causes X to lose. It's worthless for X to have a greater support in the first round, and it's harmfull if that is causing X to lose. If the actual ballot tallies are not available, a real-life election can't be modelled in examples. Guessing what the actual votes could have been is fiction and not real-life. Best, --Richard (talk) 11:08, 24 April 2014 (UTC)

2009 Burlington, Vermont mayoral election
The current version is hard to understand, but not very informative, I propose also to change this subsection as follows: A real-life monotonicity violation was detected in the 2009 Burlington, Vermont mayor election under instant runoff voting, where the necessary information is available. In this election, the winner Bob Kiss could have been defeated by raising him on some of the ballots. E.g. if all voters who ranked Kurt Wright over Bob Kiss over Andy Montroll, would have ranked Kiss over Wright over Montroll, and additionally some people who ranked only Wright, would have ranked Kiss over Wright, then these votes in favor of Kiss would have have made him lose! The winner in this scenario would have been Andy Montroll, who was also the Condorcet winner according to the original ballots.

If there are no complaints or suggestions to these three changes, I would change the article accordingly -- Richard 13:45, 13 May 2011 (UTC)

 * Richard's version seemed to have lived for a few years, but was changed by Tbouricius in diff #760704116 in January 2017. Adding the names and parties of the candidates is helpful, but it also states that instead of a real-life monotonicity violation "... was detected" it is now "...could have occurred". It also adds the sentence "This hypothetical monotonicity violating scenario, however, would require that right-leaning voters switch to the most left-wing candidate."  This wording is confusing to me; I may take a crack at rephrasing it, but it'd be wonderful if someone else who understands this better did the work. -- RobLa (talk) 21:30, 11 October 2017 (UTC)

 * Sorry that my reply is really late. I just reworded the section again and kept the information about the candidates' party affiliations, as it may be useful for readers in assessing how relevant they consider the example. But I removed the last sentence "This hypothetical monotonicity violating scenario, however, would require that right-leaning voters switch to the most left-wing candidate."
 * The alleged left-to-right order of candidates is subjective and a decisive left-to-right-sorting K,M,W isn't supported by the actual voting data (among fully ranked votes: app. ¼ of votes for Wright had Kiss 2nd and Monroe 3rd, i.e. among these app. ¼ didn't state a "right-to-left preference" W>M>K). Also added that Kiss was incumbent, and incorporated that it's a comparison of a real world election outcome to a hypothetical mono-raise alteration.
 * as alleged left-to-right order of candidates is subjective and a decisive left-to-right-sorting K,M,W isn't supported by the actual voting data (among fully ranked votes: app. ¼ of votes for Wright had Kiss 2nd and Monroe 3rd, i.e. among these --Richard (talk) 18:39, 31 August 2023 (UTC)

Real-life monotonicity violations
I have a problem with the section "Real-life monotonicity violations" and the 2009 Burlington description. AFAIK it is not a violation of monotonicity if you could adjust the vote tallies to affect the result, even if such examples show the latent possibility of such an outcome. To observe real life monotonicity you need to show change in votes between two elections. IIRC from reading the lit some years ago, that's why it's hard to find a real life example, precisely because changing patterns of votes are not so easy to detect, and it's impossible to know whether voters were switching from one candidate to another, ceteris parebus.--Red Deathy (talk) 13:44, 7 June 2011 (UTC)

 * No, you can't argue on the base of two different elections, because you can't say that voter V changed it's preferences if ballot submission is secret (what it always should be!). And you won't most likely (almost for sure) find any two real elections that fit into the mono-raise criterion ("... without changing the orders of the other candidates.", only raise one candidate, no other changes in all ballots). Best, --Richard (talk) 12:12, 24 April 2014 (UTC)

I want to question the whole existing of a "real-life monotonicity violation." Monotonicity is a mathematical property but not something that happens. If the issue is that non-monotonicity invites certain kinds of tactical voting, then state the kind of tactical voting incentives that may occur and link to the appropriate sections of the Tactical voting article. Monotonicity involves an election and a hypothetical alternative election, so it can't happen, per se, in real-life. Progressnerd (talk) 22:48, 19 November 2017 (UTC)

 * Hi, you're right in monotonicity being a property that an election method either possesses or not, and "real-life monotonicity violation" is kind of a misnomer. In the Burlington example, I now tried to phrase it better, i.e. non-monotonicity of IRV can be exemplified based on real world election data, showing it's not just some abstract mathematical property, but something which can have actual real world implications (like not having any kind of alternative votes obviously has also real life implications. And funny enough, if the Wikipedia article about the election is right, then the city switched back to a two round runoff system, which has the same type of monotonicity violations as IRV).
 * Maybe the section should be renamed to something like "monotonicity violations exemplified with real-life data".
 * But I don't consider it a good fit to just link to Tactical Voting, as the section is explicitly about how a lack of monotonicity can be exemplified when real world data is provided. And the subsection about Burlington's mayoral election exemplifies a lack of monotonicity for the most common voting system IRV.
 * illustration of IRV's lack of monotonicity using real world data (for the most common ranked voting system IRV). --Richard (talk) 19:08, 31 August 2023 (UTC)

Probability
I altered the section on probability, chiefly because it read like someone making a case, rather than an NPOV statement of the available resources, some bits sounded like OR (The section asked for a citation on still reads a little OR, but I think it deserves a chance to be substantiated).--Red Deathy (talk) 13:57, 7 June 2011 (UTC)

Runoffs are much more common than IRV, but no focus on them
Backers of single winner reforms that violate later-no-harm criteria like to focus their ire on instant runoff voting. But in fact traditional runoff elections are more likely to generate nonmonotonic outcomes than IRV because the field abruptly is reduced to just two candidates for the runoff. In typical fashion in articles developed primarily by IRV critics, the focus of this article is much more on IRV than on runoff elections. Anyone interested in providing balance by examining the huge number of runoffs around the world (most presidential elections are chosen by runoffs, for example) would be doing disinterested readers a favor. RRichie (talk) 22:13, 11 October 2012 (UTC))

 * Hi, you have a point in IRV being hypothetically less prone to monotonicity violations, yet it's even harder to exemplify it for two-round runoffs with real world data, as the information how voters would rank candidates is usually not collected. So any ranked voting system is easier to criticise, as it collects more information. And first past the post is perfect regarding monotonicity, it just fails in basically every other aspect except simplicity / ease of use (although partitioning into voting districts may spoil even the latter).
 * Two round systems with a top-two runoff are mathematically equivalent to IRV if only three candidates are running, so simple examples match both systems. My example in section "Instant-runoff voting and the two-round system are not monotonic" seems to have survived, so it's mentioned since many years.
 * Btw. there are also runoffs with up to three candidates, which possess actually an interesting feature: do not eliminate all choices except for two (with a decent chance polar opposites). Even IRV could be stopped with three candidates left, and having a second round runoff.
 * With just three candidates left, even rather complicated Descending Coalition methods (DSC&DSQ) are rather easy to describe and implement.
 * And with just three candidates, even Descending Coalitions methods (DSC/DSQ) are rather easy to describe and impleme (t. --Richard (talk) 19:48, 31 August 2023 (UTC)

Copied from Talk:STAR voting
First, I'm going to discuss the definition of the Monotonicity criterion. That article equates the term to what Woodall termed "mono-raise" in. STAR very clearly does not violate this criterion, and Markus Schulze's example above is not germane.

Woodall himself gives 7 different monotonicity criteria, of which mono-raise is only the first. Of those, STAR passes only mono-raise. I've seen other more-complete lists of monotonicity criteria which include other ones that Woodall missed and STAR passes, such as mono-add-plump (which does not imply and is not implied by mono-raise).

Is mono-raise the canonical monotonicity criterion, as the relevant wikipedia article currently states? Let's look at the other, more recent references cited by that article:

 * ... this considers only strictly ordinal rules; by the definition there, STAR is not even a voting method. Does not directly apply. However, within the limits of this constraint, the given definition of "monotonicity" is equivalent to mono-raise.
 * Ditto.
 * In formal terms, this has the same problem as the two articles above; it considers only fully-ranked voting methods. However, it does include the following less-formal (English) definition of monotonicity: "An election profile P exhibits an upward monotonicity failure if there exists a profile P� that is identical to P except that candidate A [the winner under P] is ranked higher by a subset of voters, but candidate A is not the IRV winner." Schulze is in essence arguing that the word "ranked" in this definition is absolutely key even for rated voting methods; Nardopolo is in essence arguing that this word should be replaced by "rated" when discussing rated methods. Since this definition is equivalent to mono-raise for ranked methods, I think it's evidence that unqualified "monotonicity" is generally understood to mean mono-raise; in other words, I think this should count as evidence in Nardopolo's favor.
 * This article gives only the following incomplete definition of monotonicity: "...a condition known as non-monotonicity. This has a complex definition, but is most easily explained as a condition where a candidate can increase their chances of victory by lowering their first preference count." It's clear that Antony Green does not consider this the only meaning of monotonicity, but it's also clear that STAR passes by this definition.

So all in all, I'd say that "monotonicity" is generally understood as "mono-raise", which STAR passes. Homunq (࿓) 11:22, 20 August 2018 (UTC)

 * I decided to take this further; I searched "monotonicity voting cardinal" on Google Scholar and clicked on the 6 links in the first page of results that appeared potentially relevant. These include: (sorry, Harvard proxy in urls)

 * Discusses how ordinal voting methods work for cardinal agents. Does not define "monotonic" for cardinal voting methods.
 * Doesn't mention monotonicity, don't know why it came up. (Also, a whole paper on voting dedicated to proving Pareto dominance is Unclear On The Concept. The class of situations where Pareto dominance applies has no overlap with realistic voting scenarios.)
 * Doesn't actually mention cardinal voting methods; unrelated use of "cardinal".
 * Uses cardinal mono-raise as the primary definition of monotonicity, though other definitions are discussed.
 * Defines monotonicity for ordinal methods and for approval voting. Both definitions are special cases of cardinal mono-raise.
 * Doesn't define monotonicity (only reference to it is a citation of one of Schulze's papers).

 * So, though I still don't have a slam-dunk proof that cardinal mono-raise is the best definition of "monotonic" to use here, I think this evidence further tends to support that proposition. In particular, the definition of monotonicity for approval voting is a clear counterexample to Schulze's argument that only the ordinal definition is accepted. Homunq (࿓) 14:46, 20 August 2018 (UTC)

Muller–Satterthwaite Theorem
The Muller–Satterthwaite Theorem relies on a definition of monotonicity that appears to be slightly different than the one presented here. Being more strict, it gives a much stronger result. Should the distinction be mentioned in this article? 2605:A601:A927:1900:257D:1C19:DCAC:E3EF (talk) 07:12, 17 November 2021 (UTC)
 * It sounds relevant to the page, so yes. --Erel Segal (talk) 14:39, 18 November 2021 (UTC)

State of this article
Thank you for beginning to edit this article. I think it is currently not in a good state. I however, do not quite see the reason to revert my revertion. The Frequency of Violation Section is currently not in a good state. rangevoting.org is not a source that should appear on wikipedia WP:RELIABLE. Just take a look at the Australia article, you will see that it is not a good scientific source. Further, I added an actual academic source which studied the frequency of IRV monotonicity violations, I think that would be beneficial for the article. Finally, I do not understand the figure. Either it needs some proper explanation or should be deleted.  A typical four-candidate election is not a valid explanation though. Jannikp97 (talk) 07:08, 22 March 2024 (UTC)

 * I don't have any objections to also including the academic article. That said, the work of both the Center for Range Voting and Dr. Warren D. Smith are well-known and respected in the electoral system design community. (Despite the... unusual, 2009-era web design.) Closed Limelike Curves (talk) 07:30, 22 March 2024 (UTC)
 * Sorry to say this, but I do not think this is really true. They are surely well-known, but well-respected only marginally. If we look at say WP:REPUTABLE we should cite articles that are reliable, independent, published sources with a reputation for fact-checking and accuracy. The rangevoting page satisfies none of these criteria, especially not independence and accuracy. Hence, I would prefer, if possible, to rather use reliable sources, as otherwise this might give the false impression of acknowledging the page as a wikipedia worthy source. In this article, for instance, the citation for the Burlington election can easily be replaced by the Graham-Squire and McCune paper. Further, the discussion and especially methodology on the pages on Louisiana and Australia do not seem very scientific to me, so I am not too sure about including them here. Jannikp97 (talk) 08:19, 22 March 2024 (UTC)
 * I'm not sure what makes you say the Center for Range Voting (now Center for Election Science) isn't reliable, independent, or doesn't have a reputation for fact-checking or accuracy?
 * The work they put out is pretty good, and WDS is a PhD mathematician with years working in the field. The work isn't published in a peer-reviewed journal, but preprints by scholars are commonly cited on Wikipedia. Closed Limelike Curves (talk) 21:35, 22 March 2024 (UTC)
 * The quality on the rangevoting website is notoriously low and Smith seems to put more effort into insulting established researchers, e.g., Arrow or Saari, than making his work readable. Further, the site seems to be very much focused on promoting range voting, which itself makes it not independent, but instead quite biased.
 * Smith having a PhD in math isn't really relevant (even though his old non voting work seems quite good).
 * Yes preprints are commonly cited on Wiki (whether that is a good thing is different question). However, I think usually only preprints of established researchers. For instance compare to WP:SELFPUB Jannikp97 (talk) 08:32, 23 March 2024 (UTC)
 * The figure is a Yee diagram, description here:
 * https://electowiki.org/wiki/Yee_diagram
 * Improved descriptions welcome! Closed Limelike Curves (talk) 07:32, 22 March 2024 (UTC)
 * If I had to be honest, if this article does not even manage to properly describe what this image visualizes, I am not too sure, it would be possible in an image caption. The image is certainly pretty, but at least to me it seems more-so confusing than actually helpful. Jannikp97 (talk) 08:54, 22 March 2024 (UTC)
 * As an alternative, I have this diagram which colors the win region depending on where candidate C is placed. Is this clearer?
 * Nonmonotonic.png Closed Limelike Curves (talk) 18:00, 22 March 2024 (UTC)
 * This is a bit clearer, however I am not too sure if it perfectly symbolizes monotonicity. In the figure, we are not really talking about the preferences of the voters, but the locations of the candidates or am I missunderstanding something here? Jannikp97 (talk) 18:03, 22 March 2024 (UTC)
 * Yes, you're right, although you can see it by "squinting" (the blue hole in the middle is where candidate C loses despite being the most popular candidate, but they can win by moving towards the wings). It's not as good as the current image for representing monotonicity violations, though. Closed Limelike Curves (talk) 18:19, 22 March 2024 (UTC)
 * Yeah. Probably it is fine to leave it for the time being. There are worse things to fix in voting articles :D Jannikp97 (talk) 20:24, 22 March 2024 (UTC)

title: Talk:Monotonicity criterion


text:
Daddy Wouldn't Buy Me a Bow Wow

"Daddy Wouldn’t Buy Me a Bow Wow" is a song written in 1892 by prolific English songwriter Joseph Tabrar.

It was written for, and first performed in 1892 by, Vesta Victoria at the South London Palace, holding a kitten. The same year it was recorded by Silas Leachman for the North American Phonograph Co. of Chicago (Talking Machine Company of Chicago/Chicago Talking Machine). In 1895 Toulouse-Lautrec painted May Belfort singing it. The comedian Arthur Roberts also had success in the 1890s with the song.

The song featured in the 1934 musical movie Evergreen, sung by Jessie Matthews, and was also revived after World War II.

The chorus was sung by Helen Mirren and Peter Sellers in the 1980 movie The Fiendish Plot of Dr. Fu Manchu. It is also the tune Sarah Jane Smith whistles when she leaves the Doctor at the end of the Doctor Who episode "The Hand of Fear". It is sung by the EastEnders cast, led by Anna Wing (Lou Beale, as part of the 1985 EastEnders Sing Along. In the first episode of the 1983 BBC series Reilly, Ace of Spies, one of Sidney Reilly's mistresses performs a striptease to a phonograph recording of the song.

On CD

 * A version of Vesta Victoria singing the song can be found on the CD 60 Old-Time Variety Songs ISBN 0-86175-008-X
 * It also appears on the Ultimate Pub Sing-A-Long Album

Lyrics
I love my little cat, I do With soft black silky hair It comes with me each day to school And sits upon the chair When teacher says "why do you bring That little pet of yours?" I tell her that I bring my cat Along with me because

Daddy wouldn't buy me a bow-wow! bow wow! Daddy wouldn't buy me a bow-wow! bow wow! I've got a little cat And I'm very fond of that But I'd rather have a bow-wow Wow, wow, wow, wow

We used to have two tiny dogs Such pretty little dears But daddy sold 'em 'cause they used To bite each other's ears I cried all day, at eight each night Papa sent me to bed When Ma came home and wiped my eyes I cried again and said

Daddy wouldn't buy me a bow-wow! bow wow! Daddy wouldn't buy me a bow-wow! bow wow! I've got a little cat And I'm very fond of that But I'd rather have a bow-wow Wow, wow, wow, wow

I'll be so glad when I get old To do just as I "likes" I'll keep a parrot and at least A half a dozen tykes And when I've got a tiny pet I'll kiss the little thing Then put it in its little cot And on to it I'll sing

Daddy wouldn't buy me a bow-wow! bow wow! Daddy wouldn't buy me a bow-wow! bow wow! I've got a little cat And I'm very fond of that But I'd rather have a bow-wow Wow, wow, wow, wow

title: Daddy Wouldn't Buy Me a Bow Wow