Dr Vercruyssen
email: vercruyssen@univ-tln.fr......

Objectives: To investigate the effect of cadence selection during the final minutes of cycling on metabolic responses, stride pattern, and subsequent running time to fatigue. Methods: Eight triathletes performed, in a laboratory setting, two incremental tests (running and cycling) to determine peak oxygen uptake (VO 2 PEAK) and the lactate threshold (LT), and three cycle-run combinations. During the cycle-run sessions, subjects completed a 30 minute cycling bout (90% of LT) at (a) the freely chosen cadence (FCC, 94 (5) rpm), (b) the FCC during the first 20 minutes and FCC220% during the last 10 minutes (FCC220%, 74 (3) rpm), or (c) the FCC during the first 20 minutes and FCC+20% during the last 10 minutes (FCC+20%, 109 (5) rpm). After each cycling bout, running time to fatigue (T max ) was determined at 85% of maximal velocity. Results: A significant increase in T max was found after FCC220% (894 (199) seconds) compared with FCC and FCC+20% (651 (212) and 624 (214) seconds respectively). VO 2 , ventilation, heart rate, and blood lactate concentrations were significantly reduced after 30 minutes of cycling at FCC220% compared with FCC+20%. A significant increase in VO 2 was reported between the 3rd and 10th minute of all T max sessions, without any significant differences between sessions. Stride pattern and metabolic variables were not significantly different between T max sessions. Conclusions: The increase in T max after FCC220% may be associated with the lower metabolic load during the final minutes of cycling compared with the other sessions. However, the lack of significant differences in metabolic responses and stride pattern between the run sessions suggests that other mechanisms, such as changes in muscular activity, probably contribute to the effects of cadence variation on T max .

uring triathlon racing (swim/cycle/run), the most critical and strategic aspect affecting overall performance is the change from cycling to running. [START_REF] Bentley | Specific aspects of contemporary triathlon: implications for physiological analysis and performance[END_REF][START_REF] Gottshall | The acute effects of prior cycling cadence on running performance and kinematics[END_REF][START_REF] Hausswirth | Relationships between mechanics and energy cost of running at the end of a triathlon and a marathon[END_REF][START_REF] Hausswirth | Effects of cycling alone or in a sheltered position on subsequent running performance during a triathlon[END_REF][START_REF] Vercruyssen | Influence of cycling cadence on subsequent running performance in triathletes[END_REF][START_REF] Bernard | Effect of cycling cadence on subsequent 3-km running performance in well-trained triathletes[END_REF] These studies have attempted to identify aspects of cycling that may improve running performance in triathletes. Drafting has been shown to be a beneficial cycling strategy which results in an improved subsequent running performance in elite triathletes. [START_REF] Hausswirth | Effects of cycling alone or in a sheltered position on subsequent running performance during a triathlon[END_REF] More recently, the selection of cycling cadence during a cycle-run combination has been identified by researchers as an important variable that may affect overall performance. 1 2 5 6 Cadence selection has been reported to influence metabolic responses, kinematic variables, and performance during a cycle-run session. However, the extent to which the cadence selection affects subsequent maximal running performance during a cycle-run combination remains unclear.

In a laboratory setting, Vercruyssen et al [START_REF] Vercruyssen | Influence of cycling cadence on subsequent running performance in triathletes[END_REF] have shown that the adoption of a low cadence (73 rpm), corresponding to the energetically optimal cadence, reduced oxygen uptake (VO 2 ) during a cycle-run session, compared with the selection of higher cadences (80-90 rpm). These authors suggested that the choice of a low cadence (,80 rpm) before the cycle-run transition may be advantageous for the subsequent run. However, during field based investigations, Gottshall and Palmer 2 found an improved 3200 m track running performance after 30 minutes of cycling conducted at a high cadence (.100 rpm) compared with lower cadences (70-90 rpm) for a group of triathletes. It was suggested that the selection of a high cadence improved running performance through increased stride rate and running speed during the subsequent run. In contrast, Bernard et al [START_REF] Bernard | Effect of cycling cadence on subsequent 3-km running performance in well-trained triathletes[END_REF] showed no effect of cycling cadence (60-100 rpm) and stride rate on a subsequent 3000 m running performance. These conflicting results indicate the difficulty of predicting the optimal cadence selection for a cycle-run session in trained triathletes.

In most of the above experiments, the triathletes were required to cycle at either an imposed cadence (range 60-110 rpm) or a freely chosen cadence (range 80-90 rpm) which remained constant for the entire 30 minutes of the cycle bout. This lack of cadence variation does not reproduce race situations, during which the cadence may vary considerably especially before the cycle-run transition. [START_REF] Bentley | Specific aspects of contemporary triathlon: implications for physiological analysis and performance[END_REF] Many triathletes attempt to optimise the change from cycling to running by selecting high cadences (.100 rpm) during the final kilometres of cycling. 1 2 6 Another strategy, however, may be the selection of a low cadence (,75 rpm) before the cycle-run transition, in order to conserve energy for the subsequent run. 4 5 To our knowledge, no data are available on cadence changes during the last few minutes before the cycle-run transition and its effects on subsequent running performance.

Therefore the aim of this investigation was to examine, in a laboratory setting, the effect of cadence variations during the final 10 minutes of cycling on metabolic responses, stride pattern, and subsequent running time to fatigue in triathletes.

METHODS

Participants

Eight experienced male triathletes currently in training volunteered to take part in this experiment. All had regularly competed in triathlon racing at either sprint (0.750 km swim/ 20 km cycle/5 km run) or Olympic distances (1.5

Maximal tests

Two incremental tests were used to determine peak oxygen uptake (VO 2 PEAK), maximal power output (P max ), maximal running speed (V max ), and lactate threshold (LT). Subjects performed cycling bouts on a racing bicycle mounted on a stationary turbo-trainer system. Variations in power output were measured using a ''professional'' SRM crankset system (Schoberer Rad Messtechnick, Fuchsend, Germany) previously validated in a protocol comparison using a motor driven friction brake. [START_REF] Jones | The dynamic calibration of bicycle power measuring cranks[END_REF] Running bouts were performed on a motorised treadmill situated next to the cycle turbo-trainer.

For cycling, the test bout began at an initial workload of 100 W for three minutes, after which the power output was increased by 40 W every three minutes until exhaustion. For the treadmill test, the initial running speed was fixed at 9 kph, with an increase in velocity of 1.5 kph every three minutes. For both cycling and running tests, there was a one minute rest period between each increment for the sampling of capillary blood (35 ml) from a hyperaemic earlobe. Blood samples were collected to determine plasma lactate concentration ([La 2 ]) using a blood gas analyser (ABL 625; Radiometer Medical A/S, Copenhagen, Denmark). performed 15 minutes of warm up comprising 13 minutes at a low power output (100-130 W) and the last two minutes at the individual workload required during the cycle bout of cycle-run sessions. After two minutes of rest, each triathlete completed a cycle bout at (a) the freely chosen cadence (FCC), (b) the FCC during the first 20 minutes and FCC220% during the last 10 minutes (FCC220%), or (c) the FCC during the first 20 minutes and FCC+20% during the last 10 minutes (FCC+20%). The FCC¡20% range has previously been used during a 30 minute cycling exercise in triathletes. 9 10 Cycling bouts were performed at a power output corresponding to 90 % of LT (266 (28) W) and represented an intensity close to that reported in previous studies of the relation between cycling cadence and running performance. 5 6 FCC220% was chosen to replicate cadence values close to the energetically optimal cadence previously noted in triathletes, [START_REF] Vercruyssen | Influence of cycling cadence on subsequent running performance in triathletes[END_REF] and FCC+20% allowed us to reproduce cadence values close to those reported during cycling strategies before running. 1 2 6 Cadence and power output were monitored using the SRM power meter during all cycling bouts. No feedback was given to the subjects on their FCC over the three conditions.

After each cycling bout, running time to fatigue (T max ) was determined on the treadmill at a running speed corresponding to 85% of V max (.LT) for each athlete (16.7 (0.7) kph). 11 12 During these tests, VO 2 , minute ventilation (VE), and On the basis of previous experiments and the completion respiratory exchange ratio were continuously recorded every 15 seconds using Ametek gas analysers (SOV S-3A and COV CD3A; Pittsburgh, Pennsylvania, USA). The four highest consecutive VO 2 values were summed to determine VO 2 PEAK. [START_REF] Bishop | The relationship between plasma lactate parameters, Wpeak and endurance cycling performance[END_REF] P max and V max were calculated as the average power output and running speed in the last three minutes completed before exhaustion. Heart rate (HR) was monitored every 10 seconds during each experimental session using an electronic HR device with a chest electrode (Polar Vantage NV; Polar Electro Oy, Kempele, Finland). The LT calculated by the modified D max method was determined by the point on the polynomial regression curve that yielded the maximal perpendicular distance to the straight line formed by the lactate inflection point (first increase in lactate concentration above the resting level) and the final lactate point. [START_REF] Bishop | The relationship between plasma lactate parameters, Wpeak and endurance cycling performance[END_REF] Cycle-run combinations All triathletes completed, in random order, three cycle-run sessions each composed of 30 minutes of cycling, on a cycle turbo-trainer, and a subsequent run to fatigue. A fan was used in front of the subject during these experimental sessions. Before each experimental condition, subjects of pilots tests, this running intensity was chosen to induce fatigue in less than 20 minutes. All subjects were given verbal encouragement throughout each trial. The T max was taken as the time at which the subject's feet left the treadmill as he placed his hands on the guardrails. The transition time between running and cycling was fixed at 45 seconds to reproduce the racing context. 1 6 Measurement of metabolic variables VO 2 , VE, and HR were monitored and analysed during the following intervals: 3rd-5th minute of cycling bout (3-5 min), 20th-22nd minute (20-22 min), 28th-30th minute (28-30 min) and every minute during the running sessions. Five blood samples were collected at the following intervals: before the warm up, at 5, 20, and 30 minutes during cycling, and at the end of T max .

Measurement of kinematic variables

Power output and cycling cadence were continuously recorded during the cycling bouts. For each running session, a 50 Hz digital camera was mounted on a tripod 4 m away from the motorised treadmill. Subsequently, the treadmill speed and period between two ground contacts for the same foot were determined using a kinematic video analysis system (SiliconCoach Pro Version 6, Dunedin, New Zealand). From these values, stride pattern characteristicsthat is, stride rate (Hz) and stride length (m)-were calculated every 30 seconds during the first five minutes and the last two minutes of the T max sessions.

Statistical analysis

All data are expressed as mean (SD). A two way variance analysis plan with repeated measures was performed to analyse the effects of cadence selection (FCC, FCC220%, FCC+20%) and time during the cycle-run sessions using VO 2 , VE, HR, [La 2 ], stride rate, stride length, cadence and power

Cycling bouts of cycle-run sessions

No significant variation in FCC was observed during the first 20 minutes of the three cycling bouts (table 2). In addition, mean power output values were not significantly different between the cycling bouts (264 (30), 263 (28), and 261 (29) W respectively for FCC, FCC220%, and FCC+20%). These data show that subjects adhered to the experimental design with respect to the required power output-cadence combination.

A significant effect of exercise duration (between 3-5 and 28-30 min intervals) was observed on VO 2 , VE, and HR during the FCC and FCC+20% bouts whereas no significant variation in these metabolic variables was identified with exercise duration during the FCC220% condition (table 3). Moreover, mean VO 2 , VE, and HR were significantly lower at FCC220% compared with FCC+20% during the 28-30 min interval (respectively, 25.3%, 218.2%, and 26.8%). [La 2 ] was significantly higher during the 28-30 min interval at FCC+20% compared with FCC (+31.2%) or FCC220% (+55.5%).

Running bouts of cycle-run sessions

A significant increase in T max was observed only after the FCC220% modality when compared with both the FCC+20% and FCC conditions (+43.3% and +37.3% respectively; fig 1). T max values were 624 (214), 651 (212) and 894 (199) seconds after the FCC+20%, FCC and FCC220% modalities respectively. A significant increase in DVO 2 -that is, between the 3rd and 10th minute-was found during the T max completed after FCC (+6.1%), FCC+20% (+6.7%), and FCC220% (+6.5%) (table 4). However, mean VO 2 , VE, HR, and [La 2 ] were not significantly different between the three T output, as dependent variables. A Tukey post hoc test was sessions (table 4). max used to determine any differences between the cycle-run combinations. Differences in T max obtained between the three experimental conditions were analysed by one way analysis of variance. A paired t test was used to analyse differences in VO 2 PEAK, HR peak , and VO 2 at LT between the two maximal tests. Statistical significance was set at p,0.05.

RESULTS

Maximal tests

No significant differences in VO 2 PEAK were observed between the sessions (table 1). However, HR peak and VO 2 at LT were significantly higher during running than during the maximal cycling bout (+2.9% and +15.8% respectively).

No significant difference in stride pattern was observed during the T max sessions whatever the prior cadence selection (fig 2). Mean stride rate (Hz) and stride length (m) were 1.49 (0.01) and 3.13 (0.02), 1.48 (0.01) and 3.13 (0.03), 1.49 (0.01) and 3.15 (0.02), during the T max sessions subsequent to the FCC, FCC220% and FCC+20% bouts respectively.

DISCUSSION

The main findings of this investigation show a significant increase in T max when the final 10 minutes of cycling is performed at FCC220% (894 seconds) compared with FCC (651 seconds) and FCC+20% (624 seconds). Several hypotheses are proposed to explain the differences in T max reported during the various cycle-run combinations for the group of triathletes.

A number of studies have analysed characteristics of cyclerun sessions in triathletes, with particular focus on physiological and biomechanical aspects during the subsequent run. [START_REF] Bentley | Specific aspects of contemporary triathlon: implications for physiological analysis and performance[END_REF] For instance, during a running session after cycling, a substantial increase in energy cost, VE, and HR, and differences in muscle blood flow have been observed compared with an isolated run. 1 3 5 6 Moreover, variations in running kinematics such as stride rate, segmental angular position, and joint angle have been shown after a cycle bout. 3 5 These running alterations, which have been linked to the effects of exercise duration and cycle-run transition, were reported during treadmill sessions conducted at a submaximal intensity and not during a high intensity running bout. In this study we investigated these effects at a high intensity close to a running speed previously observed during a short cycle-run combination in triathletes. [START_REF] Bernard | Effect of cycling cadence on subsequent 3-km running performance in well-trained triathletes[END_REF]

Metabolic hypotheses

The T max values of this investigation are comparable to those previously reported during an exhaustive isolated run performed at an intensity corresponding to 85-90% VO 2 MAX. [START_REF] Avogadro | Changes in mechanical work during severe exhausting running[END_REF][START_REF] Billat | The VO2 slow component for severe exercise depends on type of exercise and is not correlated with time to fatigue[END_REF][START_REF] Candau | Energy cost and running mechanics during a treadmill run to voluntary exhaustion in humans[END_REF] It has previously been reported that metabolic and muscular factors are potential determinants of middle distance running performance and/or exhaustive treadmill sessions in trained subjects. [START_REF] Borrani | Is the VO2 slow component dependent on progressive recruitment of fast-twitch fibers in trained runners?[END_REF][START_REF] Brandon | Physiological factors associated with middle distance running performance[END_REF][START_REF] Paavolainen | Neuromuscular characteristics and muscle power as determinants of 5-km running performance[END_REF][START_REF] Paavolainen | Neuromuscular characteristics and fatigue during 10 km running[END_REF][START_REF] Prampero | Factors limiting maximal performance in humans[END_REF] With respect to metabolic factors, the improvement in T max observed after FCC220% may be related to changes in energy contribution. In support of this hypothesis, it has been reported that the determinants of maximal performances in middle distance running may be linked to the energy requirement for a given distance and the maximal rate of metabolic energy output from the integrative contribution of aerobic and anaerobic systems. 15 18 During submaximal and maximal running, the VO 2 variation has been reported to reflect the relative contribution from the aerobic and anaerobic sources. [START_REF] Brandon | Physiological factors associated with middle distance running performance[END_REF] In the context of a cycle-run session, Bernard et al [START_REF] Bernard | Effect of cycling cadence on subsequent 3-km running performance in well-trained triathletes[END_REF] have reported that triathletes were able to sustain a higher fraction of VO 2 MAX during a 3000 m track run performed after cycling at 60 rpm than during cycling at 80 and 100 rpm. These authors suggested that a greater contribution of the aerobic component, during running after the choice of a low cadence, may delay fatigue for longer running distances. In this investigation, the analysis of VO 2 may also provide information on possible changes in aerobic contribution during high intensity running. Given the range of T max values, the metabolic variables were analysed during the first 10 minutes of each running session, corresponding approximately to the mean T max values reported after the FCC and FCC+20% modalities (fig 1). The evaluation of this time interval indicates no significant differences in VO 2 between the T max sessions, suggesting that the determination of T max in this study was not affected by changes in metabolic energy from the aerobic or anaerobic systems.

There was, however, a significant increase in VO 2 between the 3rd and 10th minute (6.1-6.7%) during the three T max sessions, regardless of the prior experimental condition (table 4). During exercise lasting less than 15 minutes, the continual rise in VO 2 beyond the 3rd minute has been termed the VO 2 slow component (VO 2SC ). 5 11 19 20 The occurrence of a VO 2SC is classically observed during heavy running and cycling exercises associated with a sustained lactic acidosis-that is, above the LT. 19 21 22 Postulated mechanisms responsible for this VO 2SC include rising muscle temperature (Q 10 effect), cardiac and ventilatory muscle work, lactate kinetics, catecholamines, and recruitment of less efficient type II muscle fibres. [START_REF] Poole | Determinants of oxygen uptake[END_REF] Within this framework, Yano et al [START_REF] Yano | Relationship between the slow component of oxygen uptake and the potential reduction in maximal power output during constant-load exercise[END_REF] suggested that muscular fatigue may be one of the factors that produce the development of a VO 2SC during high intensity cycling exercise.

However, several investigators have examined the influence of prior exercise on the VO 2 response during subsequent exercise. [START_REF] Burnley | Effects of prior heavy exercise on phase II pulmonary oxygen uptake kinetics during heavy exercise[END_REF][START_REF] Gerbino | Effects of prior exercise on pulmonary gasexchange kinetics during high-intensity exercise in humans[END_REF][START_REF] Scheuermann | The slow component of O2 uptake is not accompanied by changes in muscle EMG during repeated bouts of heavy exercise in humans[END_REF] Burnley et al [START_REF] Burnley | Effects of prior heavy exercise on phase II pulmonary oxygen uptake kinetics during heavy exercise[END_REF] showed that the magnitude of VO 2 kinetics during heavy exercise was affected only by a prior bout of heavy exercise. On the basis of similar results, it has been suggested that, during successive bouts of heavy exercise, muscle perfusion and/or O 2 off loading at the during the second bout of exercise. 25 26 In addition, changes in the VO 2 response may be accentuated by the manipulation of cadence during an isolated cycling bout. [START_REF] Gotshall | Cycling cadence alters exercise hemodynamics[END_REF] Gotshall et al [START_REF] Gotshall | Cycling cadence alters exercise hemodynamics[END_REF] showed an increase in muscle blood flow and a decrease in systemic vascular resistance with increasing cadence (from Stride rate (Hz) 70 to 110 rpm). These previous experimental designs, based on the characteristics of combined and isolated exercises, are similar to the current one and suggest that cadence selection may affect blood flow and hence the VO 2 response during a subsequent run. For instance, the increased muscle blood flow at high cycling cadence [START_REF] Gotshall | Cycling cadence alters exercise hemodynamics[END_REF] during a prior cycle bout could attenuate the magnitude of VO 2SC during subsequent running.

In contrast with these earlier studies, the VO 2SC values of this investigation were not significantly different between trials during the first 10 minutes of exercise between the T max sessions. This was observed despite differences in metabolic load and cadence selection during the previous cycling bouts. These results indicate that the adoption of FCC220% is associated with a reduction in metabolic load with exercise duration, but does not affect the VO 2SC during the subsequent run. For instance, the selection of FCC220% is associated with a significant reduction in VO 2 (25.3%), VE (218.2%), HR (26.8%), and [La 2 ] (255.5 %) during the final 10 minutes of cycling compared with FCC+20%, without any significant changes in VO 2SC during subsequent running between the two conditions. This suggests that the chosen cadences do not affect the VO 2 responses during the subsequent run and also that the occurrence of a VO 2SC does not contribute to the differences in T max found in this study. This is consistent with previous research on trained subjects. [START_REF] Billat | The VO2 slow component for severe exercise depends on type of exercise and is not correlated with time to fatigue[END_REF] Muscular and stride pattern hypotheses Although we conducted no specific analysis of muscular parameters, an attractive hypothesis to explain the differences in T max between conditions is that they are due to differences in the muscular activity or fatigue state during cycle-run sessions. Muscular contractions differ during cycling and running. Cycling is characterised by longer phases of concentric muscular contraction, whereas running involves successive phases of eccentric-concentric muscular action. [START_REF] Bijker | Differences in leg muscle activity during running and cycling in humans[END_REF] Muscle activity during different modes of contraction can be assessed from the variation in the electromyographic signal. In integrated electromyography based investigations, it has been shown that muscles such as the gastrocnemius, soleus, and vastus lateralis are substantially activated during running. 14 17 28 Any alterations in the contractile capability of these muscles may have affected the ability to complete a longer T max during the cycle-run sessions in this study.

Furthermore, many studies have reported substantial changes in muscular activity during isolated cycling exercises, especially when cadence is increased or decreased. [START_REF] Ericson | Muscular activity during ergometer cycling[END_REF][START_REF] Marsh | The relationship between cadence and lower extremity EMG in cyclists and noncyclists[END_REF][START_REF] Neptune | The effect of pedaling rate on coordination in cycling[END_REF][START_REF] Takaishi | Optimal pedaling rate estimated from neuromuscular fatigue for cyclists[END_REF] With respect to the cycle-run combination, the manipulation of cadence may accentuate modifications in muscular activity during cycling and influence the level of fatigue during a subsequent run. Marsh and Martin [START_REF] Marsh | The relationship between cadence and lower extremity EMG in cyclists and noncyclists[END_REF] showed a linear increase in electromyographic activity of the gastrocnemius and vastus lateralis muscles when cadences increased from 50

What this study adds

This study shows that the choice of a low cadence during the final minutes of cycling improves subsequent running time to fatigue.

to 110 rpm. Although activity of the gastrocnemius muscle has been shown to increase considerably more than the soleus muscle as cadence is increased, 30 31 Ericson et al [START_REF] Ericson | Muscular activity during ergometer cycling[END_REF] have also reported a significant increase in soleus muscle activity with the selection of high cadences. These results from isolated cycling exercises conducted in a state of non-fatigue suggest that, during the last 10 minutes of the cycling bout of our study, there was greater recruitment of the vastus lateralis, gastrocnemius, and soleus muscles after cycling at higher cadences. This may have resulted in an increase in fatigue of these muscles, which are substantially activated during subsequent running. In contrast, the lower activity of the vastus lateralis, gastrocnemius, and soleus muscles after the FCC220% condition may have reduced the fatigue experienced during cycling and resulted in improved utilisation of these muscles during the subsequent run. This may have contributed to the observed increase in T max for this condition. Nevertheless, Lepers et al 10 suggested that the neuromuscular fatigue observed after 30 minutes of cycling was attributable to both central and peripheral factors but was not influenced by the pedalling rate in the range FCC¡20%. In this earlier study, the selected power outputs (.300 W) for all cadence conditions were significantly higher than those used in our experiment (260-265 W). The choice of high power outputs during cycling 10 may result in attenuation of the differentiated effects of extreme pedalling cadences on the development of specific neuromuscular fatigue. Further research is required to analyse the relation between various pedalling strategies and muscular recruitment patterns specific to a short cycle-run session (,1 hour).

The analysis of movement patterns during the cycle-run sessions also indicates that possible changes in muscle activity may be associated with modifications in kinematic variables. [START_REF] Hausswirth | Relationships between mechanics and energy cost of running at the end of a triathlon and a marathon[END_REF] Hausswirth et al 3 reported significant variations in stride rate-stride length combination during a run session subsequent to a cycling bout compared with an isolated run. These modifications were attributed to local muscle fatigue from the preceding cycle. In the present study, the absence of significant differences in stride pattern during running (fig 2), regardless of the prior cadence selection, indicates that there is no relation between stride pattern and running time to fatigue. These results are consistent with previous results from a laboratory setting where the running speed was fixed on a treadmill after various cadence selections. [START_REF] Vercruyssen | Influence of cycling cadence on subsequent running performance in triathletes[END_REF] In contrast, in field based investigations, in which the running speed and stride pattern were freely selected by the athletes, Gottshall and Palmer 2 found that cycling at 109 rpm, compared with 71 and 90 rpm, during a 30 minute cycle session resulted in an increased stride rate and running speed during a 3200 m track session. However, these results are in contrast with those of Bernard et al [START_REF] Bernard | Effect of cycling cadence on subsequent 3-km running performance in well-trained triathletes[END_REF] indicating an effect of the prior cadence on stride pattern only during the first 500 m and not during the overall 3000 m run. The relation between stride pattern, cycling cadence, and running performance is not clear. Further investigation is required to elucidate the mechanisms that affect running performance during a cycle-run session.

In conclusion, this study shows that the choice of a low cadence during the final minutes of cycling improves subsequent running time to fatigue. The findings suggest What is already known on this topic Various characteristics of cycle-run sessions in triathletes have been studied, with particular focus on physiological and biomechanical aspects during the subsequent run. During a running session after cycling, a substantial increase in energy cost, minute ventilation, and heart rate, and differences in muscle blood flow have been observed compared with an isolated run. Moreover, variations in running kinematics such as stride rate, segmental angular position, and joint angle have been shown after a cycle bout.

that metabolic responses related to VO 2 do not explain the differences in running time to fatigue. However, the effect of cadence selection during the final minutes of cycling on muscular activity requires further investigation. From a practical standpoint, the strategy to adopt a low cadence before running, resulting in a lower metabolic load, may be beneficial during a sprint distance triathlon.

Figure 1

 1 Figure 1 Running time to fatigue after the selection of various cycling cadences. Values are expressed as mean (SD). *Significantly different from the other sessions, p,0.05.

1 TFigure 2

 12 Figure 2 Variations in stride rate during the running time to fatigue after the selection of various cycling cadences. T, Stride rate obtained at Tmax; T21, stride rate obtained at Tmax -1 min; T22, stride rate obtained at T max -2 min.

Table 2

 2

	Cadence and power output values during the
	three cycling bouts at different time periods: 3-5, 20-22,
	28-30 min
	Cycling bout	Cadence (rpm)	Power output (W)
	FCC220%
	Values are mean (SD).
	*Significantly different from the first 20 minutes, p,0.05.
	*Significantly different from the other conditions at the same time period,
	p,0.05.

Table 3

 3 Variations in mean oxygen uptake (VO 2 ), minute ventilation (VE), heart rate (HR), and blood lactate concentration ([La 2 ]), during the three cycling bouts, at different time periods: 3-5,20-22, 28-30 min

	Values are expressed as mean (SD).
	*Significantly different from the 3-5 min interval, p,0.05.
	*Significantly different from the 20-22 min interval, p,0.05.
	`Significantly different from FCC220% at the same period, p,0.05.
	1Significantly different from FCC+20% at the same period, p,0.05.

Table 4

 4 Variations in mean oxygen uptake (VO 2 ), DVO 2 (10-3 min), minute ventilation (VE), heart rate (HR), and blood lactate concentration ([La 2 ]) during the three running sessions performed after cycling

	Values are expressed as mean (SD).
	*Significantly different between the 3rd and 10th minute of exercise, p,0.05.

ACKNOWLEDGEMENTS

We gratefully acknowledge all the triathletes who took part in the experiment for their great cooperation and motivation. . . . . . . . . . . . . . . . . . . . . . Authors' affiliations F Vercruyssen, J Brisswalter, Department of Sport Ergonomics and Performance, University of Toulon-Var, BP 132, 83957 La Garde cedex, France R Suriano, D Bishop, School of Human Movement and Exercise Science, University of Western Australia, Crawley, WA 6009, Australia C Hausswirth, Laboratory of Physiology and Biomechanics, Nationale Institute of Sport and Physical Education, 11, avenue du Tremblay, 75 012 Paris, France

Competing interests: none declared


Emmanuel Flachaire

Guillaume Hollard
email: hollard@univ-mlv.fr

Individual sensitivity to framing effects by

Keywords: starting-point bias, wta-wtp divergence, social representation JEL Classification: C81, C90, H43, Q51

come

Introduction

It has long been recognized that the design of a survey may influence respondents' answers. In the particular case in which respondents have to estimate numerical values, this implies that two different surveys may lead to two different valuations of the same object. Such a variation of answers, induced by non-significant change in the survey design, is called a framing effect. Consequently, surveys are sometimes viewed with suspicion when used to provide economic values, since framing effects may alter the quality of survey-based valuation. The existence of these effects is well documented [START_REF] Levin | All frames are created equal : a typology and critical analysis of framing effects[END_REF]. However, the extent to which they may vary between individuals has received little attention. Are some individuals less sensitive to framing effects than others ? How to detect them ? These are the questions addressed in this paper.

Our basic idea is to use the theory of social representation to assign to each individual a new variable. This variable represents a proxy for the individual's sensitivity to framing effects. According to this representation variable, we isolate two types of individuals. The first type is proved to be less sensitive to framing effects than the other. We examine two framing effects which are known to have a dramatic effect on valuation, namely, starting-point bias and willingness to pay (WTP) and willingness to accept (WTA) divergence. The results suggest that taking into account heterogenous sensitivity to framing effects is successful in limiting the impact of biases. Furthermore, they prove that the constructed representation variable is not correlated to any of the usual variables. Thus, using the representation variable allows researchers to gather relevant new information.

The paper is organized as follows. Section 2 details how social representation can be used to design a new individual variable. Section 3 presents study of the problem of starting-point bias in contingent valuation surveys. Section 4 deals with WTA and WTP divergence. Section 5 provides a discussion, and Section 6 concludes.

Representation as a source of heterogeneity

Representations are defined in a broad sense by social psychologists as a form of knowledge that serves as a basis for perceiving and interpreting reality, as well as for guiding one's behavior. Representation could concern a specific object, or a more general notion of social interest1 . The founding work [START_REF] Moscovici | La psychanalyse, son image et son public[END_REF] explores the representation of psychoanalysis. In the following decades, various topics have been investigated: representation of different cities, madness, remarkable places, hunting, AIDS, among others (see the different articles presented in Farr and[START_REF] Farr | Social representations[END_REF][START_REF] Moscovici | Psychologie Sociale[END_REF]. The theory of representation has proved useful in the study of economic subjects such as saving and debt [START_REF] Viaud | A positional and representational analysis of consumption: Households when facing debt and credit[END_REF], or the electronic purse [START_REF] Penz | It's practical but no more controllable": Social representation of the electronic purse in Austria[END_REF].

The basic structure of a social representation is composed of a central core and of peripheral elements [START_REF] Abric | Central system, peripheral system : their fonctions and roles in the dynamics of social representation[END_REF]. The central core contains the most obvious elements commonly associated with the object. They can be viewed as stereotypes or common sense. Those elements are not subject to any dispute, as everyone agrees that they are related to the object described. The core in itself does not contain much information and usually is not a surprise to an observer. The peripheral elements, however, contain fewer consensual elements and are less obvious. They represent potential changes in the social representation and indicate new elements that may in the near future become part of the core. They are, somehow, rivals of the core elements.

There are several ways to explore the composition of social representations of particular subjects (namely, ethnography, interviews, focus-groups, the content analysis of the media, questionnaires and experiments). In what follows, we will focus on a particular technique, which is the statistical analysis of word associations. These word associations are gathered through answers to an open-ended question such as "What are the words that come to mind when thinking of [the object]?" or "What does [the object] evoke to you?". Thus, the purpose of such questions is to investigate the words being spontaneously associated with a given object. The next step is thus to determine the core of the social representation, on the basis of those individual answers. Once the core has been found, we sort individuals according to those who refer to the core of the social representation and those who don't. This "aller-retour" between social and individual representations can be compared to an election system where individual opinions are aggregated, using majority voting. Once individuals have voted, it is possible to recognize who belongs to the majority and who doesn't. All in all, the task is to transform representations (i.e. lists of words) into a quantitative and individual variable.

The method consists of four steps, each of which is illustrated with an example, namely the Camargue representation 2 . The Camargue is a major wetland in the delta of the Rhône (south of France) covering 75.000 hectares. Of exceptional biological diversity, it hosts many fragile ecosystems and is inhabited by numerous species. The survey was administered to 218 visitors to the Camargue at the end of their visit 3 . Note that the respondents had therefore spent some time in the Camargue.

Step 1: The data: collecting lists of words

The usual way to collect information on representation is by open-ended questions. More precisely, we use a question such as: "What does [the object] evoke to you?" or "What are the words that come to mind when thinking of [the object]?". Individuals are expected to provide a list of words or expressions. Thus, the data take the form of ordered lists of words. The set of answers typically displays a large number of different words, as each individual provides different answers. Indeed, a great variety of words can be used to describe a given object [START_REF] Vergès | Approche du noyau central: propriétés quantitatives et structurales[END_REF][START_REF] Wagner | Theory and method of social representations[END_REF].

Application: In our questionnaire, respondents were asked: "What words come to your mind when you think about the Camargue?" More than 300 different words or expressions have been obtained.

Step 2: Classification: choosing a typology for words An individual representation is captured through an ordered list of words. The high number of different words (say 100 to 500) imposes a categorization, i.e. putting together words that are "close" enough. Choosing a particular categorization thus consists in defining a particular typology for the set of words. Empirical applications typically use six to ten categories, which are chosen so as to form homogeneous categories. This step is the only one which leaves the researcher with some degree of freedom, since the notion of proximity is not straightforward.

After categorization, each individual's answer is transformed into an ordered list of categories (rather than a list of words). At the end of this categorization, we are left with individual representations containing doubles, that is, with several attributes belonging to the same category. To obtain transitive individual representations, we suppress the lower-ranking citations belonging to the same category. Such treatment eliminates some information. In our case, the length of individual answers decreased by 20%.

After treatment (i.e. categorization + suppression of doubles), individual representations boil down to an individual ranking of the set of categories.

Application: A basic categorization by frame of reference leads to eight different categories. For instance, the first category is called Fauna and Flora. It contains all the attributes which refer to the animals and local vegetation of the Camargue (fauna, 62 citations, birds, 44, flora, 44, bulls, 37, horses, 53, flamingos, 36, . . . ). The other categories are Landscape, Disorientation, Isolation, Preservation, Human presence and Coast. A particular case is the category Nature which only contains the word nature which can hardly fall into any of the previous categories. There is a ninth category which clusters all attributes which do not refer to any of the categories mentioned above4 .

Step 3: Finding the core

The simplest way of determining the core element is to classify the different categories according to their citation rate. The core is thus composed of the category that is most widely used by individuals. This is in accordance with the definition of the core as the most consensual and widely accepted elements associated with a given object.

Application: After consolidating the data in step 2, we were left with 218 ordered lists of categories. We computed the number of appearances for each category. The results are presented in Step 4: Sorting individuals

We choose to isolate individuals who do not mention the top element of the social representation (i.e. the core of the social representation). This leads to a breakdown of individuals into two sub-samples: one which contains the individuals who used the core element in their representation, and one which contains the individuals who did not.

The main reason for this is that it is remarkable not to mention any of the core elements. It is thus assumed that not mentioning the core is indeed significant. Since it does not conform to most common practice, this group is often referred to as "minority". The other group, which mentions the core element, is referred to as "mainstream".

Application: In the case of the Camargue, the subjects were interviewed at the end of their visit and had seen a lot of animals and plants (they could even see some of them while being interviewed). A small minority of individuals did not refer to Fauna and Flora (18% of the total population, see Table 1).

Given these four steps, we are left with two categories of individuals. This leads to a breakdown of individuals into two sub-samples: those who refer to the core of the social representation (mainstream) and the others (minority). We can define a mainstream dummy variable, which can be used to control the sensitivity to framing effects. To do so, existing models have to be adapted. In the following, we use this new variable with empirical data, considering two standard framing effects, starting point bias and WTA-WTP divergence.

Starting-point bias

In contingent valuation, respondents are asked if they are willing to pay a fixed sum of money for a given policy to be implemented. This discrete choice format is recommended by the NOAA panel over other methods (a panel of experts that sets guidelines to run evaluation surveys, see [START_REF] Arrow | Report of the NOAA panel on contingent valuation[END_REF]. This "take it or leave it" format mimics a market situation which individuals face in everyday market transactions, and it is incentive-compatible. However, a major drawback is that it leads to a qualitative dependent variable (the respondent answers yes or no), which reveals little about the individual's willingness-to-pay (WTP). To gather more information on respondents' WTP, [START_REF] Hanemann | Some issues in continuous and discrete response contingent valuation studies[END_REF] and [START_REF] Carson | Three essays on contingent valuation (welfare economics, non-market goods, water quality[END_REF] proposed adding a follow-up discrete choice question to improve the efficiency of discrete choice questionnaires. This mechanism is known as the double bounded model. It basically consists of proposing a second bid to the respondent, greater than the first bid, if the respondent's first answer is yes, and lower otherwise.

Several studies have found that estimates of the mean of willingness-to-pay are substantially different from estimates based on the first question alone. This is the so-called starting-point bias [START_REF] Herriges | Starting point bias in dichotomous choice valuation with follow-up questioning[END_REF], which can be seen as a particular case of the anchoring bias put forward by [START_REF] Tversky | Judgment under uncertainty: Heuristics and biases[END_REF] 6 . Different models have been proposed in the litterature to control for such undesirable effects. However, empirical results suggest that efficiency gains obtained with follow-up questions are lost relative to models using first questions only. All these models assume that all individuals are equally sensitive to starting-point bias. In this section, we consider that some individuals may be more sensitive than others to starting-point bias. We develop a model to handle starting-point bias with heterogeneity in two groups. An application shows that, with individual sensitivity to starting-point bias, we can control for starting-point bias with efficiency gains.

Model

Different models are proposed in the literature to control for starting-point bias in double-bounded models. All these models assume that the second answer is sensitive to the first bid offer, in the sense that a prior willingness-to-pay W i is used by the respondent i to respond to the first bid offer, b 1i , and an updated willingness-to-pay W ′ i is used to respond to the second bid, b 2i . Each model leads to a specific definition of W ′ i . Whitehead ( 2002) proposes a general model, combining several effects, as follows:

W ′ i = W i + γ (b 1i -W i ) + δ, (1)
where γ and δ are two parameters. If δ = 0 this model corresponds to the Anchoring model proposed by [START_REF] Herriges | Starting point bias in dichotomous choice valuation with follow-up questioning[END_REF], where the respondents combine their prior WTP with the value provided by the first bid, such that the first bid offer plays the role of an anchor. The parameter γ measures the strength of the anchoring effect (0 ≤ γ ≤ 1). If γ = 0 this model corresponds to the Shift model proposed by [START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF], where the WTP systematically shifts between the two answers. The first bid offer is thus interpreted as providing information about the cost or the quality of the object: a respondent can interpret a higher bid offer as paying more for the same object and a lower bid offer as paying less for a lower quality object. The model (1) combines both Anchoring and Shift effects.

In model ( 1), all individuals are supposed to be sensitive to the first bid offer in the same manner: the two parameters γ and δ are constant across individuals. If only some respondents are influenced by the first bid (i.e. they combine their prior WTP with the first bid), while the others do not, individual heterogeneity is present. It is well known that econometric estimation of regression models can be seriously misleading if such heterogeneity is not taken into account. Let us assume that we can divide respondents into two distinct groups: one group subject to starting-point bias and another insensitive. We define a Heterogenous model as

W ′ i =    W i if I i = 0 W i + γ (b 1i -W i ) + δ if I i = 1 (2)
where I i is a dummy variable which is equal to 1 when individual i belongs to one group and 0 if he belongs to the other group. Note that, if I i = 1 for all respondents, this model reduces to the Anchoring & Shift model ; if I i = 0 for all respondents, it reduces to the standard Double-bounded model.

These models can be estimated with random effect probit models, taking into account the dynamic aspect of follow-up questions [START_REF] Cameron | Estimation using contingent valuation data from a dichotomous choice with follow-up questionnaire[END_REF][START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF], Whitehead 2004). Estimation requires simulated methods and a formal definition of the probability that the individual i answers yes to the j th question, j = 1, 2. For the heterogenous model (2), we calculate this probability, which is equal to:

P (W ji > b ji ) = Φ X i α - 1 σ b ji + θ (b 1i -b ji )I i D j + λI i D j (3)
where D 1 = 0 and D 2 = 1, α = β/σ, θ = γ/(σγσ) and λ = δ/(σγσ). Based on this equation, the parameters are interrelated according to:

β = ασ, γ = θσ/(1 + θσ) and δ = λσ(1 -γ). (4)
Implementation of the Double-bounded model is obtained with δ = γ = 0, which corresponds to θ = λ = 0 in (3). Implementation of the Anchoring & Shift model is obtained with I i = 1 for i = 1, . . . , n. For a more detailed discussion on the estimation of a random effect probit model, see [START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF]Whitehead (2004).

Results

We use the dummy variable mainstream, defined in the previous section, and the Camargue survey to conduct an application. In practice, a value of particular interest is the estimate of the WTP mean. Once a model has been estimated, we can obtain fitted values Ŵi , for i = 1, . . . , n, from which we can calculate the estimate of the mean of WTP: μ = n -1 n i=1 Ŵi . We estimate the mean values of WTP from a linear model (MacFadden and Leonard 1993) and compute the confidence intervals by simulation with the Krinsky and Robb procedure (see Haab and McConnell 2003, ch.4). The Single-bounded and Double-bounded models give very different WTP means: 113.5 and 89.8. Their confidence intervals do not overlap. Such inconsistent results suggest that follow-up questions generate starting-point bias in the Double-bounded model.

To control for starting-point bias, we estimate an Anchoring & Shift model. The WTP mean is equal to 158.5. It is still very different from the WTP mean obtained from the Single-bounded model (113.5); however, the two confidence intervals overlap slightly. Note that the confidence interval is very wide and the gain in precision obtained by using follow-up questions is lost, a result suggested by [START_REF] Herriges | Starting point bias in dichotomous choice valuation with follow-up questioning[END_REF].

The Heterogeneous model gives a WTP mean of 110.1. It is very close to the 113.5 obtained from the Single-bounded model. Moreover, the confidence interval obtained from the Heterogeneous model ([99.0; 125.2]), is entirely contained in the confidence interval obtained from the Single-bounded model ([98.1; 138.2]), and thus is narrower. In other words, the Heterogeneous model provides consistent results with the Single-bounded model, and is more precise. Table 3 presents the full econometric results, that is, all the parameter estimates, with the standard errors given in italics. It is clear from this table that using follow-up questions (Double-bounded, Anchoring & Shift and Heterogenous models) provides significantly reduced standard errors, compared to using first answers only (Single-bounded model). Moreover, the precision of the parameter estimates of the regressors is quite similar for the different models using follow-up questions. The anchoring parameter γ is statistically significant when we perform a likelihood-ratio (LR) test of the null hypothesis γ = 0, not the shift parameter δ. It suggests that, when the minority group is not sensitive to starting-point bias (γ = 0, see equation 2), the mainstream group is significantly subject to such an effect (γ = 0.26, with 0 ≤ γ ≤ 1).

Finally, the Heterogeneous model performs better than the others: it provides consistent results with the Single-bounded model and greatly improves the precision of the estimation. This suggests that taking into acount an individual sensitivity to startingpoint bias does indeed matter.

WTA and WTP divergence

Over the past twenty years, a large pattern of empirical evidence has accumulated suggesting a significant divergence between willingness-to-pay (WTP) measures of value, where individuals have to pay for a given object or policy, and willingness-to-accept (WTA) measures of value, where individuals sell the same object or receive money to compensate for the suppression of the same policy [START_REF] Brookshire | Measuring the value of a public good: an empirical comparaison of elicitation procedures[END_REF]. Economic theory suggests that, with small income effects, WTP and WTA should be equivalent. Results from a meta-analysis however prove that the divergence, measured by the ratio WTA/WTP, is often high (i.e. the ratio largely exceeds one) [START_REF] Sayman | Effects of study design characteristics on the wtawtp disparity: a meta analytical framework[END_REF]. Since valuation measures are used for the study of many public-policy questions, these results raise questions about which procedure to use in practice.

The divergence is frequent but can be controlled for. The existence of substitutes has been proved to play an important role [START_REF] Shogren | Resolving differences in willingness to pay and willingness to accept[END_REF]). In the case of private goods the divergence disappears if subjects are recruited among experienced dealers [START_REF] List | Does market experience eliminate market anomalies?[END_REF][START_REF] List | Neoclassical theory versus prospect theory: evidence from the marketplace[END_REF]. This suggests that individuals may learn to avoid the divergence. This intuition is confirmed by the design of an experimental protocol that eliminates the divergence [START_REF] Plott | The willingness to pay/willingness to accept gap, the endowment effect, subject misconceptions and experimental procedures for eliciting valuations[END_REF]. The basic ingredients of this protocol are the existence of training rounds and the use of incentive-compatible mechanisms. Taken together, the previous results suggest that subjects may learn to overcome the divergence within a short period of time. These results, however, apply to private goods. If we consider the valuation of some public policy, the time between the survey and the implementation of the policy is too long to implement training rounds. This is the reason why being able to detect subjects who are prone to framing effects is of particular interest for contingent valuations.

Survey

To measure the discrepancy between WTA and WTP for public goods, we needed to find a public good that can be sold or withdrawn, or bought or provided. Such public goods are not the most common ones. However, we were lucky enough to be offered a golden opportunity. The University of Marne la Vallée (France) was considering changing its Saturday morning classes policy. The growing number of students led to an increasing number of classes on Saturday morning due to the lack of available classrooms. Students started to protest and asked for a clarification of the policy regarding classes on Saturday morning. Two options were considered. Some students were told they would pay lower fees if they accepted classes scheduled on Saturday. The reason for this was that the university could then rent the extra classroom during the week to movie companies to use for filming on location. Other students were offered the option of avoiding Saturday classes by paying higher fees, as the university would have to rent an extra building. So, the trade-off was between paying more to avoid Saturday classes and being paid to attend them. Note that, even though the survey concerned students, it was used to take a real decision. Thus, answers to this particular survey had an impact on the respondents' welfare.

We conducted a contingent valuation survey to evaluate both the willingness to pay to avoid classes on Saturday and the willingness to accept classes on Saturday morning. The survey was given to 359 students at the University of Marne La Vallée: 184 individuals were given the WTP version, 175 the WTA one (subjects were randomly assigned to one version).

Heterogeneity

Gathering information on social representations using an additional open-ended question leads to our four-step methodology. We propose here to simplify this treatment by running this methodology on a sample of subjects, at a pre-test stage, to identify the items that capture most of the opposition between mainstream and minority. This allows us to detect mainstream and minority using a simple discrete choice question. This greatly simplified the exploitation of the data. While the use of an open-ended question implies a specific treatment (categorization and so on), the use of a simple question does away with the need for any treatment.

Prior to the survey, we then elicited the representations "of classes on Saturday morning". Quite surprisingly, the survey revealed two groups that differ more broadly on their vision of university rather than on their vision of Saturday morning (we were expecting more precise reasons, such as the opportunity to have a job on Saturday morning, religious reasons). For the mainstream, the main goal of their studies is to get diplomas, while the minority consider that the most important thing to get from university is skills. Following our method, we then decided to include in the contingent valuation survey an additional question labeled as follows:

In your opinion, the main purpose of your studies is to get:

diplomas 2. skills

The two items were presented in a random order. As expected, a large majority of 71% of the 359 respondents, chose the first option (diplomas). And only a minority chose the second option (skills). We now propose to explore the impact of this distinction on the WTA-WTP divergence. If we neglect the distinction among respondents, the WTA and WTP means are very different, respectively equal to 68.7 and 15.3. The WTA/WTP ratio largely exceeds one and is equal to 4.5. Then, we calculate the WTA and WTP means for individuals who answered the questiondiplomas and skills -separately. When we consider the mainstream group (Diplomas), the discrepancy between WTA and WTP is wide and the ratio higher (5.8). However, when we consider the minority group (Skills), the discrepancy and the ratio (2.7) are significantly reduced. Students from the minority group are less sensitive to the WTA and WTP divergence. Even if the discrepancy is not completely removed, the mainstream variable allows us to separate the whole population into two groups that highly differ in their sensibility to framing effects, since the ratio is falling from 5.8 for the mainstream group to 2.7 for the minority.

Results

Further results and discussion

The previous results show that it is possible to extract information on individual representation for a given object, which can be successfully used as a good proxy for the individual sensibility to framing effects. Evidence was presented for two distinct sets of data and two different well-known framing effects. So far, we have basically found a statistically significant relationship between the mainstream variable and the sensitivity to framing effects. The remaining question is thus why does this occur? The first section proves that the representation variable conveys new information, which is not related to other individual characteristics. The second section proposes an interpretation of the link between social representation and framing effects. General considerations on social representation are given in a third section. The last section deals with possible improvements to the proposed approach.

Does representation provide new information ?

Here, we check if the dummy variable, based on social representation, is correlated with some other individual characteristics. First consider the Camargue survey. Table 5 shows the Pearson correlation coefficient ρ between the mainstream dummy variable and the regressors included in the regression model. A P -value is given in parenthesis for the null hypothesis ρ = 0. We can see that in all cases, the null is rejected (all the P-values are greater than 0.05). It suggests that the dummy variable is not correlated to the regressors.

Secondly, consider the Saturday classes survey. Table 6 shows the Pearson correlation coefficient ρ between the Diplomas/Skills dummy variable and other questions from the questionnaire. A P -value is given in parenthesis for the null hypothesis ρ = 0. We can see that in all cases, the null is rejected (all the P-values are greater than 0.05). Again, it suggests that the dummy variable is not correlated to the regressors. These results suggest that the information obtained from individual representation cannot be captured by the use of standard individual characteristics. In this sense, it is new information, not related to standard questions in surveys.

From representation to framing effects

So far, we have concentrated on the most technical aspects, based on statistical evidence. Here, we propose an interpretation about why representations can be linked to framing effects. This interpretation relies on three distinct arguments. The first two are nothing more than an application of general ideas developed in psychology and sociology. The key argument is thus the third one.

1. Our use of social representation is very classical on some points and more original on others. Identifying the core and peripheral elements of a social representation on the basis of a statistical analysis of word associations is a classic in social psychology. It is also admitted that peripheral elements are identified by a minority. Our approach thus consists in pooling all minorities in one group.

2. The next step of our reasoning is to assume that these individuals are conscious of not being members of the mainstream, while others may just follow the crowd with no clear consciousness of doing so. The idea that members of the minority have a more accurate perception of their identity is generally accepted in sociology. Thus, we associate a classical sociological argument with a more psychological one.

3. The core idea of our work is that the minority group on a particular subject has a stronger opinion, i.e. a more personal or elaborate point of view 7 . Thus, the minority is more likely to resist outside influences and is therefore less sensitive to framing effects.

Representation as a marker of past experience

If you have never coped with an object or a situation in the past in the past, you are very likely to handle it at first glance in a very predictable way, using common sense or stereotypes. This is what the core represents. But, if for any reason, you have been confronted with this problem in the past, it is very likely that you start recomposing your representation of this object or situation (you don't have the same representation of Paris once you've been there). According to that view, non-mainstream representations are then a consequence of past experiences. Representations can thus be thought of as a fast and frugal way to capture information about past experiences.

If we now concentrate on the problem of eliciting preferences (say for public decision making), representations allow us to isolate individuals that have somehow "invested" in their own preference. We expect them to hold a stronger opinion and have more stable preferences, thus be less sensitive to framing effects. Such a distinction is similar to the debate on the origin of individual preferences [START_REF] Slovic | The construction of preference[END_REF]. Members of the minority are assumed to be individuals that have set their preferences, while some members of the mainstream population are assumed to construct their preferences through the elicitation process. Our results suggest how to identify individuals that have set their preferences before the elicitation process begins. The existence of such a population is not a surprise since in any experiments that intend to detect biases, a small, but significant, part of the subjects do not exhibit pathological preferences (among many references, see the experiments in [START_REF] Kahneman | Choices, Values and Frames[END_REF]. This paper is a first step towards detecting such individuals.

Criticism, improvements and further research

The proposed method has reached the goal of proving that a substantial heterogeneity relative to the sensitivity to framing effects exists, even in socially very homogenous populations such as students. The agenda for further research includes the design of more subtle tools to classify individuals. Here, we are able to isolate a population that is prove to be much less sensitive to framing effects than the residual population. One can think of a more continuous variable that measures the sensitivity to framing effects. a strong point of view.

The proposed methodology is open to criticism at two distinct levels. As we are exploiting an open-ended question, a choice has to be made on how to categorize the answers. A good classification requires the creation of homogeneous categories. Even though our classification8 tends to demonstrate the presence of individual sensitivity to framing effects, another choice could be considered. A second criticism may concern the way we construct the two subpopulations on the basis of the social representation. Our choice is to put respondents who cite the most cited category in a mainstream group, and the others in the minority group. Other choices and alternatives splits (with more than two groups) could be used. Finally, our dichotomous split has done a good job as a first step, but further research may help us to better understand the determinants of individual sensitivity to framing effects.

Conclusion

This paper is a first step towards approaching heterogeneity relative to the sensitivity to framing effects. A simple tool is designed to detect a group of individuals that is proved to be far less sensitive to framing effects than the reference population. This approach is effective on two distinct sets of data concerning different framing effects. This raises important questions at the normative level. How should values be set within heterogeneous groups ? Should the values be computed using only the values of those detected as not sensitive to framing effects ?

Table 1 .

 1 The top element, Fauna-Flora, is used by a large number of

	Category	Citation Rate Rank
	Fauna-Flora	82 %	1
	Landscape	74 %	2
	Isolation	58 %	3
	Preservation	51 %	4
	Human presence	34 %	5
	Nature	33 %	6
	Disorientation	32 %	7
	Coast	26 %	8

Table 1 :

 1 Citation Rank respondents, 82%. Only a minority do not use any element of this category. This is not a big surprise since the main interest of the Camargue (as presented in all related commercial publications, or represented on postcards) is the Fauna and Flora category 5 .

Table 2 :

 2 Table 2 presents estimates of the WTP mean, obtained from the Double-bounded, Anchoring & Shift and Heterogeneous models. We include estimates obtained from the Single-bounded, taking into account the first answers only. The analysis is based on two criteria: if the mean of WTP is consistent (consistency) and if the standard errors are more precise (efficiency) with those obtained from the Single-bounded model. Estimation of the mean of willingness-to-pay

	Model	WTP mean conf. interval consistency efficiency
	Single-bounded	113.5	[98.1;138.2]
	Double-bounded	89.8	[84.4;96.5]	no	yes
	Anchoring & Shift	158.5	[122.6;210.7]	yes	no
	Heterogeneous	110.1	[99.0;125.2]	yes	yes

Table 3 :

 3 Random effects probit models (standard errors in italics)

Table 4 :

 4 Table4shows the WTP and WTA means for all the students (384, 175 for the WTA version and 184 for the WTP version) and for the two sub-groups (those who answer Diplomas and those who answer Skills). The last line presents the WTA/WTP ratio. WTA/WTP divergence

	All Diplomas Skills
	WTA 68.7	71.9	62.5
	WTP 15.3	12.5	23.3
	Ratio 4.5	5.8	2.7

Table 5 :

 5 The Camargue survey: correlation coefficient.

Table 6 :

 6 Saturday classes survey: correlation coefficient.

A survey of the theory and methods used to study social representations can be found in[START_REF] Wagner | Theory and method of social representations[END_REF] and[START_REF] Canter | Empirical approaches to social representation[END_REF]

This method was originally developed in[START_REF] Flachaire | A new approach to anchoring: theory and empirical evidence from a contingent valuation survey[END_REF]

See Claeys-Mekdade et al. (1999) for a complete description of the survey

After categorization and deletion of doubles, the average number of attributes evoked by the respondents falls

from 5.5 to 4.0. 5 A quick look at any website about the Camargue is also a way of confirming Fauna-Flora as the obvious aspect of the Camargue. Among many others see: www.parc-camargue.fr or www.camargue.com

The anchoring bias appears in experimental settings in which subjects are asked to provide numerical estimations (e.g. the height of Mount Everest). Prior to the estimation stage, they are asked to compare their value to an externally provided value (e.g. 20 000 feet). This last value received the name of anchor as it was proved to have a great influence on subjects' valuations (i.e. a different anchor, or starting point, leads to a different valuation)

Note that we do not exclude that some individuals may have a strong point of view which is in accordance with that of the mainstream. We only suggest that we can isolate some individuals holding

A full description of the one we used is available in[START_REF] Hollard | Théorie du choix social et représentations : analyse d'une enquête sur le tourisme vert en camargue[END_REF]

Whitehead, J. C. (2004). Incentive incompatibility and starting-point bias in iterative valuation questions: reply. Land Economics 80 (2), 316-319.

Acknowledgements

The authors thank Jason Shogren for useful comments and two anonymous referees.