Keywords: starting point bias, preference uncertainty, contingent valuation JEL Classification: Q26, C81

Introduction

The NOAA panel recommends the use of a dichotomous choice format in contingent valuation (CV) surveys. This format has several advantages: it is incentive-compatible, simple and cognitively manageable. Furthermore, respondents face a familiar task, similar to real referenda. The use of a single valuation question, however, presents the inconvenience of providing the researcher with only limited information. To gather more information, [START_REF] Hanemann | Statistical efficiency of doublebounded dichotomous choice contingent valuation[END_REF] proposed adding a follow-up question. This is the double-bounded model. This format, however, has been proved to be sensitive to starting point bias, that is, respondents anchor their willingness-to-pay (WTP) to the bids. It implies that WTP estimates may vary as a function of the bids. Many authors propose some specific models to handle this problem [START_REF] Herriges | Starting point bias in dichotomous choice valuation with follow-up questioning[END_REF][START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF][START_REF] Deshazo | Designing transactions without framing effects in iterative question formats[END_REF][START_REF] Whitehead | Incentive incompatibility and starting-point bias in iterative valuation questions[END_REF][START_REF] Cooper | One and one-half bids for contingent valuation[END_REF][START_REF] Flachaire | Controlling starting-point bias in double-bounded contingent valuation surveys[END_REF]. The behavioral assumption behind these models is that respondents hold a unique and precise willingness-to-pay prior to the survey. Observed biases are interpreted as a distortion of this initial willingness-to-pay during the survey.

Independently, several studies document the fact that individuals are rather unsure of their own willingness-to-pay [START_REF] Li | Discrete choice under preference uncertainty: an improved structural model for contingent valuation[END_REF][START_REF] Ready | Contingent valuation when respondents are ambivalent[END_REF], 2001[START_REF] Welsh | Elicitation effects in contingent valuation: comparisons to a multiple bounded discrete choice approach[END_REF][START_REF] Van Kooten | Preference uncertainty in non-market valuation: a fuzzy approach[END_REF][START_REF] Hanley | What's it worth? Exploring value uncertainty using interval questions in contingent valuation[END_REF][START_REF] Alberini | Analysis of contingent valuation data with multiple bids and response options allowing respondents to express uncertainty[END_REF].

To account for such uncertainty, these studies allow respondents to use additional answers to valuation questions. Rather than the usual "yes", "no" and "don't know" alternatives, intermediate responses, such as "probably yes" or "probably no", are allowed. Alternatively, an additional question asks respondents how certain they are of their answers and provides a graduated scale.

In contingent valuation, starting-point bias and respondent's uncertainty have been handled in separate studies. In this article we develop a dichotomous choice modelhereafter called the Range model -in which individuals hold a range of acceptable values, rather than a precisely defined value of their willingness-to-pay. The range model is drawn from the principle of coherent arbitrariness, suggested by Ariely et al. (2003b). Prior to the survey, the true willingness to pay is assumed to be uncertain in an interval with upper and lower bounds. Confronted with the first valuation question, respondents select a value and then act on the basis of that selected value. Because of this initial uncertainty, the initial choice is subject to starting point bias. In contrast, the subsequent choices are no longer sensitive to the bid offers. A clear-cut prediction follows: biases occur within a given range and affect the first answer only. The Range model thus provides an alternative interpretation of the starting point bias in the dichotomous choice valuation surveys.

An empirical study is presented to compare various models, using the well-known Exxon Valdez contingent valuation survey. Results show that a special case of the proposed Range model, in which a "yes" response is given when the bid value falls within the range of acceptable values, is supported by the data, i.e. when uncertain, individuals tend to say "yes".

The article is organized as follows. The following section presents the Range model and the respondent's decision process. The subsequent sections provide estimation details, give further interpretation and present an application. Conclusions appear in the final section.

The Range model

The Range model derives from the principle of "coherent arbitrariness" (Ariely et al. 2003b). These authors conducted a series of valuation experiments (i.e. experiments in which the subjects have to set values for objects they are not familiar with). They observed that "preferences are initially malleable but become imprinted (i.e. precisely defined and largely invariant) after the individual is called upon to make an initial decision". But, prior to imprinting, preferences are "arbitrary, meaning that they are highly responsive to both positive and normative influences".

In a double-bounded CV survey, two questions are presented to respondents. The first question is "Would you agree to pay x$?". The second, or follow-up, question is similar but asks for a higher bid offer if the initial answer is yes and a lower bid offer otherwise. Confronted with these iterative questions, with two successive bids proposed, the principle of coherent arbitrariness leads us to consider a three-step decision process:

1. Prior to a valuation question, the respondent holds a range of acceptable values 2. Confronted with a first valuation question, the respondent selects a value inside that range 3. The respondent answers the questions according to the selected value.

The following subsections detail each step.

A range of acceptable values

At first, let us assume that a respondent i does not hold a precise willingness-to-pay but rather an interval of acceptable values:

wtp i ∈ W i , W i with W i -W i = δ. (1)
The lower bound and the upper bound are different for each respondent, but we assume the width of the range δ to be constant across individuals.1

Several psychological and economic applications support this idea. For instance, [START_REF] Tversky | Judgment under uncertainty: Heuristics and biases[END_REF] and Ariely et al. (2003bAriely et al. ( , 2003a) ) suggest the existence of such an interval. In addition, several studies in contingent valuation explore response formats that allow for the expression of uncertainty, among others see [START_REF] Li | Discrete choice under preference uncertainty: an improved structural model for contingent valuation[END_REF], [START_REF] Ready | Contingent valuation when respondents are ambivalent[END_REF], Welsh andPoe (1998), van Kooten et al. (2001), [START_REF] Hanley | What's it worth? Exploring value uncertainty using interval questions in contingent valuation[END_REF] and [START_REF] Alberini | Analysis of contingent valuation data with multiple bids and response options allowing respondents to express uncertainty[END_REF]. These studies also conclude that there is a range of values for which respondents are uncertain.

Selection of a particular value

Confronted with a first bid offer b 1i a respondent i selects a specific value inside his range of acceptable values W i , W i . The selection rule can take different forms. We propose a selection rule in which the respondent selects a value so as to minimize the distance between his range of willingness-to-pay and the proposed bid:

W i = Min wtp i |wtp i -b 1i | with wtp i ∈ W i , W i . (2)
This selection rule has attractive features. It is very simple and tractable. It is also in accordance with the literature on anchoring, which states that the proposed bid induces subject to revise their willingness to pay as if the proposed bid conveyed some information about the "right" value [START_REF] Chapman | Anchoring, activation, and the construction of values[END_REF]. At a more general level, the literature on cognitive dissonance suggests that subjects act so as to minimize the gap between their own opinion and the one conveyed by new information.

In this range model the first bid plays the role of an anchor: it attracts the willingnessto-pay. A different b 1i results in the selection of a different value W i . Thus, this selection rule should exhibit a sensitivity of the first answer to the first bid, that is, an anchoring effect. Consequently, it is expected to produce anomalies such as starting point bias.

Answers to questions

The last step of the decision process deals with the respondent's answer to questions. It is straightforward that a respondent will answer yes if the bid is less than the lower bound of his range of acceptable value W i . And he will answer no if the bid is higher than the upper bound of his range W i . However, it is less clear what is happening when the bid belongs to the interval of acceptable values.

-Answers to the first question -

A respondent i will agree to pay any amount below W i and refuse to pay any amount that exceeds W i . When the first bid belongs to his interval of acceptable values, he may accept or refuse the bid offer. Here, we do not impose a precise rule: respondents can answer yes or no with any probability when the bid offer belongs to the interval. If the bid belongs to the range of acceptable values, respondents answer yes to the first question with a probability ξ and no with a probability 1 -ξ. Thus, the probability that a respondent i will answer yes to the first question is equal to:2

P (yes) = P (b 1i < W i ) + ξ P (W i < b 1i < W i ) with ξ ∈ [0, 1]. (3)
In other words, a respondent's first answer is yes with a probability 1 if the bid is below his range of acceptable values and with a probability ξ if the bid belongs to his range. A ξ close enough to 1 (resp. 0) means that the respondent tends to answer yes (resp. no) when the bid belongs to the range of acceptable values. Estimation of the model will provide an estimate of ξ.

-Answers to follow-up questions -

The uncertainty that arises in the first answer disappears in the follow-up answers. A respondent answers yes to the follow-up question if the bid b 2i is below his willingness-topay, W i > b 2i ; and no if the bid is above his willingness-to-pay, W i < b 2i (by definition, the follow-up bid is higher or smaller than the first bid, that is b 2i = b 1i ).

Estimation

In this section, we present in detail how to estimate the Range model. It is assumed that if the first bid b 1i belongs to the interval of acceptable values of respondent i, [W i ; W i ], he will answer yes with a probability ξ and no with a probability 1 -ξ. We can write these two probabilities as follows:

ξ = P (W i < b 1i < W ξ i ) P (W i < b 1i < W i ) and 1 -ξ = P (W ξ i < b 1i < W i ) P (W i < b 1i < W i ) , (4)
with

W ξ i ∈ [W i ; W i ].
Note that, when ξ = 0 we have W ξ i = W i , and when ξ = 1 we have W ξ i = W i . From ( 4) and (3), the respondent i answers yes or no to the first question with the following probabilities

P (yes) = P (W ξ i > b 1i ) and P (no) = P (W ξ i ≤ b 1i ). ( 5
)
It is worth noting that these probabilities are similar to the probabilities derived from a single-bounded model with W ξ i assumed to be the willingness-to-pay of respondent i. It follows that the mean value of WTPs obtained with a single-bounded model would correspond to the mean of the W ξ i in our model, for i = 1, . . . , n. The use of follow-up questions will lead us to identify and estimate ξ and to provide a range of values rather than a single mean of WTPs.

If the initial bid belongs to his range of acceptable values, respondent i selects the value W i = b 1i , see (2). If his first answer is yes, a follow-up higher bid b h 2i > b 1i is proposed and his second answer is necessarily no, because W i < b h 2i . Conversely, if his first answer is no, a follow-up lower bid b l 2i < b 1i is proposed and his second answer is necessarily yes, because W i > b l 2i . It follows that, if the first and the second answers are similar, the first bid is necessarily outside the interval [W i ; W i ] and the probabilities of answering no-no and yes-yes are respectively equal to

P (no, no) = P (W i < b l 2i ) and P (yes, yes) = P (W i > b h 2i ). ( 6
)
If the answers to the initial and the follow-up questions are respectively yes and no, two cases are possible: the first bid is below the range of acceptable values and the second bid is higher than the selected value W i = W i , otherwise the first bid belongs to the range of values. We have

P (yes, no) = P (b 1i < W i < b h 2i ) + ξ P (W i < b 1i < W i ) (7) = P (b 1i < W i < b h 2i ) + P (W i < b 1i < W ξ i ) (8) = P (W i < b h 2i ) -P (W ξ i < b 1i ). (9)
Similarly, the probability that respondent i will answer successively no and yes is:

P (no, yes) = P (b l 2i < W i < b 1i ) + (1 -ξ) P (W i < b 1i < W i ) (10) = P (W ξ i < b 1i ) -P (W i < b l 2i ). (11)
To make the estimation possible, a solution would be to rewrite all the probabilities in terms of W ξ i . In our model, we assume that the range of acceptable values has a width which is the same for all respondents. It allows us to define two parameters:

δ 1 = W i -W ξ i and δ 2 = W i -W ξ i . ( 12
)
Note that δ 1 ≤ 0 and δ 2 ≥ 0 because 12) in ( 6), ( 9) and ( 11), we have

W ξ i ∈ [W i ; W i ]. Using (
P (no, no) = P (W ξ i < b l 2i -δ 2 ), P (no, yes) = P (b l 2i -δ 2 < W ξ i < b 1i ), (13)
P (yes, yes) = P (W ξ i > b h 2i -δ 1 ), P (yes, no) = P (b 1i < W ξ i < b h 2i -δ 1 ). ( 14
)
Let us consider that the willingness-to-pay is defined as,

W ξ i = α + X i β + u i , u i ∼ N (0, σ 2 ), ( 15
)
where the unknown parameters β, α and σ 2 are respectively a k × 1 vector and two scalars, X i is a 1 × k vector of explanatory variables. The number of observations is equal to n and the error term u i is Normally distributed with a mean of zero and a variance of σ 2 . This model can easily be estimated by maximum likelihood, using the log-likelihood function

l(y, β) = n i=1
r 1i r 2i log P (yes, yes) + r 1i (1 -r 2i ) log P (yes, no)

+ (1 -r 1i ) r 2i log P (no, yes) + (1 -r 1i ) (1 -r 2i ) log P (no, no) , (16)
where r 1 (resp. r 2 ) is a dummy variable which is equal to 1 if the answer to the first bid (resp. to the second) is yes, and is equal to 0 if the answer is no. To estimate our model, we can derive from ( 13) and ( 14) the probabilities that should be used:

P (no, no) = Φ[(b l 2i -δ 2 -α -X i β)/σ], (17)
P (no, yes) = Φ[(b 1i -α -X i β)/σ] -Φ[(b l 2i -δ 2 -α -X i β)/σ], (18)
P (yes, no) = Φ[(b h 2i -δ 1 -α -X i β)/σ] -Φ[(b 1i -α -X i β)/σ], (19)
P (yes, yes) = 1 -Φ[(b h 2i -δ 1 -α -X i β)/σ]. (20)
Non-negativity of the probabilities ( 18) and ( 19) require respectively b 1i > b l 2i -δ 2 and b h 2i + δ 1 > b 1i . We have defined δ 1 ≤ 0 and δ 2 ≥ 0, see ( 12): in such cases the probabilities ( 18) and ( 19) are necessarily positive. However, the restrictions δ 1 ≤ 0 and δ 2 ≥ 0 are not automatically satisfied in the estimation. To overcome this problem, we can consider a more general model, for which our Range model becomes a special case.

Interrelation with the Shift model

It is worth noting that the probabilities ( 13) and ( 14) are quite similar to the probabilities derived from a Shift model [START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF], but in which we consider two different shifts. Indeed, in a Shift model, respondents are supposed to answer the first question with a prior willingness-to-pay W i and the second question with an updated willingnessto-pay defined as:

W ′ i = W i + δ. ( 21
)
The probability of answering successively yes and no is:

P (yes, no) = P (b 1i < W i ∩ W ′ i < b h 2i ) = P (b 1i < W i < b h 2i -δ), (22)
which is equal to the corresponding probability in ( 14) with δ = δ 1 . Similar calculations can be made for the other probabilities, to show that the Range model can be estimated as a model with two different shifts in ascending/descending sequences. The underlying decision process is very different from the one developed in the Range model. In the Shift model, respondents answer questions according to two different values of WTP, W i and W ′ i . The first bid offer is interpreted as providing information about the cost or the quality of the object. Indeed, 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. Alternatively, a higher bid can make no sense to the individual, if delivery was promised at the lower bid. [START_REF] Cameron | Estimation using contingent valuation data from a dichotomous choice with follow-up questionnaire[END_REF] propose taking into account the dynamic aspect of followup questions: they suggest specification allowing the initial and follow-up answers to be based on two different WTP values. The WTP is broken down in two parts, a fixed component and a varying component over repeated questions. The random effect model can be written:

Random-effect model

W 1i = W ⋆ i + ε 1i W 2i = W ⋆ i + ε 2i
where

W ⋆ i = α + X i β + ν i . ( 23
)
The difference between the two WTP values is due to the random shocks ε 1i and ε 2i , assumed to be independent. The fixed component W ⋆ i can be split into two parts. X i β represent the part of the willingness-to-pay due to observed individual specific characteristics. ν i varies with the individual, but remains fixed over the indivual's responses: it relates unobserved individual heterogeneity and introduces a correlation between W 1i and W 2i . The correlation is high (resp. low) if the variance of the fixed component is large (resp. small) relative to the variance of the varying component, see [START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF] for more details. At the limit, if the two WTP values are identical, W 1i = W 2i , the correlation coefficient is equal to one, ρ = 1. [START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF] have modified this random-effect model to the case of the Shift model. Since the Range model can be estimated as a model with two different shifts in ascending/descending sequences (see above), the use of a random-effect model in the case of the Range model is straightforward. From equations ( 17), ( 18), ( 19) and ( 20), we can write the probability that the individual i answers yes to the j th question, j = 1, 2:

P (W ji > b ji ) = Φ [(α + X i β -b ji + δ 1 D j r 1i + δ 2 D j (1 -r 1i )) /σ] , (24)
where D 1 = 0, D 2 = 1, and r 1i equals 1 if the answer to the first question is yes and 0 otherwise. Consequently, the Range model can be estimated from the following bivariate probit model:

P (yes, yes) = Φ [α 1 + X i θ + γ b 1i ; α 2 + X i θ + γ b 2i + λ r 1i ; ρ ] . (25)
The parameters are interrelated according to:

α = -α 1 /γ, β = -θ/γ, σ = -1/γ, δ 1 = -λ/γ and δ 2 = (α 1 -α 2 )/γ. ( 26
)
Estimation with a bivariate probit model based on equation ( 25) does not impose any restriction on the parameters. The Range model is obtained if δ 1 ≤ 0 and δ 2 ≥ 0; the Shift model is obtained if δ 1 = δ 2 . It is clear that the Range model and the Shift model are non-nested; they can be tested through (25).

Interpretation

We have seen above that the estimation of the Range model derives from a general model, that also encompasses the Shift model proposed by [START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF], see ( 25) and ( 26). Estimation of model ( 15), based on equation ( 25), provides estimates of α, β, σ, δ 1 and δ 2 , from which we can estimate a mean µ ξ and a dispersion σ of the willingness-to-pay - [START_REF] Hanemann | The statistical analysis of discrete response CV data[END_REF] by

µ ξ = n -1 n i=1 W ξ i = n -1 n i=1 (α + X i β). ( 27
)
This last mean of WTPs would be similar to the mean of WTPs estimated using the first questions only, that is, based on the single-bounded model.

Additional information can be obtained from the use of follow-up questions: estimates of δ 1 and δ 2 allows us to estimate a range of means of WTPs. The mean value of WTPs estimated from our model µ ξ is the mean of the estimates of W ξ i for all the respondents, i = 1, . . . , n. From ( 12), we can derive the lower bounds of the range of acceptable values for all respondents and a mean of WTPs associated with it:

µ 0 = n -1 n i=1 W i = n -1 n i=1 (W ξ i + δ 1 ) = µ ξ + δ 1 , δ 1 ≤ 0. ( 28
)
It would be the mean of WTPs when respondents always answer no if the bid belongs to their range of acceptable value. Similarly, we can derive the upper bounds of their range,

µ 1 = n -1 n i=1 W i = n -1 n i=1 (W ξ i + δ 2 ) = µ ξ + δ 2 , δ 2 ≥ 0. (29)
It follows that we can provide a range of means of WTPs

[µ 0 ; µ 1 ] = [µ ξ + δ 1 ; µ ξ + δ 2 ]
with δ 1 ≤ 0, and δ 2 ≥ 0.

This range can be estimated with μξ , δ1 and δ2 . The lower bound µ 0 corresponds to the case where respondents always answer no if the bid belongs to the range of acceptable values (ξ = 0). Conversely, the upper bound µ 1 corresponds to the case where respondents always answer yes if the bid belongs to the range of acceptable values (ξ = 1). How respondents answer the question when the bid belongs to the range of acceptable values can be tested as follows:

• respondents always answer no corresponds to the null hypothesis H 0 : δ 1 = 0,

• respondents always answer yes corresponds to the null hypothesis H 0 : δ 2 = 0.

Finally, an estimation of the probability ξ would be useful. For instance, we could conclude that when the first bid belongs to the range of acceptable values, respondents answer yes in (100 ξ) % of cases. If the first bids are drawn randomly from a probability distribution, ξ can be rewritten

ξ = P (µ 0 < b 1i < µ ξ ) P (µ 0 < b 1i < µ 1 ) . (31)
In addition, if the set of first bids are drawn from a uniform distribution by the surveyors, it can be estimated by ξ = δ1 /( δ1 -δ2 ).

Application

Since independent variables other than the bid are not needed to estimate the Range model, we can use data from previously published papers on this topic. In this application, we use data from the well-known Exxon Valdez contingent valuation survey. 3 The willingness-to-pay question asked how the respondent would vote on a plan to prevent another oil spill similar in magnitude to the Exxon Valdez spill. Details about the Exxon Valdez oil spill and the contingent valuation survey can be found in [START_REF] Carson | Contingent valuation and lost passive use: Damages from the Exxon Valdez oil spill[END_REF]

Results

With the assumption that the distribution of WTP is lognormal, results in Alberini et al. show evidence of a downward shift. Here, we consider the more general model given in ( 25) from which the Double-bounded, Shift and Range models are special cases.

Estimation results are given in Table 1. We use the same model as in Alberini et al.: there are no covariates and the distribution of the WTP is assumed lognormal (θ = 0 and b ij are replaced by log b ij in ( 25)). The mean of log WTP is given by α = -α 1 γ and the median of WTP is given by exp(α). Estimation results of the Single-bounded model are obtained from a probit model. Estimation results obtained from a bivariate probit model with no restrictions in (25) are presented in column M ; the Double-bounded model is obtained with δ 1 = δ 2 = 0 ; the Shift model is obtained with δ 1 = δ 2 and the Range yes model is obtained with δ 2 = 0. -1345.70 -1303.36 -1301.32 -1301.45 Note: standard errors are in italics; n.c.: no constraints.

From Table 1, we can see that the estimates of the mean of log WTP in the Singlebounded and Double-bounded models are very different (3.727 vs. 3.080). Such incon-sistent results lead us to consider the Shift model to control for such effects. It is clear that the estimates of the mean of log WTP in the Single-bounded model and in the Shift model are very close (3.727 vs. 3.754), and that the Double-bounded model does not fit the data as well as the Shift model. Indeed, we reject the null hypothesis δ 1 = 0 from a likelihood-ratio test (LR = 84.68 and P < 0.0001). 4 To go further, we consider estimation results obtained from the model defined in (25) with no restrictions (column M). On the one hand, we reject the null hypothesis δ 1 = δ 2 from a likelihood-ratio test (LR = 4.08 and P = 0.043). It suggests that the Shift model does not fit the data as well as model M. On the another hand, we cannot reject the null hypothesis δ 2 = 0 (LR = 0.26 and P = 0.61). It leads us to select the Range yes model hereafter.

The estimated values of the parameters δ 1 and δ 2 allow us to interpret the model as a Range model (δ 1 ≤ 0, δ 2 = 0). Respondents are unsure of their willingness-to-pay in an interval; they answer yes if the initial bid offer belongs to their interval of acceptable values. We compute an interval of the median WTP:

[exp(α -δ1 ); exp(α -δ2 )] = [9.45; 44.21].

(32)

This interval suggests that, if the respondents answer no if the initial bid belongs to their range of acceptable values, the median WTP is equal to 9.45; if the respondents answer yes if the initial bid belongs to their range of acceptable values, the median WTP is equal to 44.21 (see Section 4).

Main findings

From these empirical results, we select the Range yes model, with an interval of the median WTP [9.45;44.21]. Previous researchers have also found that, when uncertain, individuals tend to say yes [START_REF] Ready | How do respondents with uncertain willingness to pay answer contingent valuation questions?[END_REF]. New with the Range model is the fact that no additional question such as "how certain are you of your answer?" is required.

From our results, several conclusions can be drawn:

1. From the Range yes model, we cannot reject the null hypothesis ρ = 1.5 This result has an important implication. It suggests that the underlying decision process defined in the Range model is supported by the data. Confronted with an initial bid, respondents select a value, then they answer both the first and the second questions according to the same value (see Sections 2 and 3.2). This is in sharp contrast to the existing literature that explains anomalies by the fact that respondents use two different values to answer the first and follow-up questions. 6 The Range model supports the view that anomalies can be explained by a specific respondent's behavior prior to the first question, rather than by a change between the first and the second questions.

2. As long as the Range yes model is selected, the Single bounded model is expected to elicit the upper bound of the individual's range of acceptable WTP values. Indeed, in the case of Exxon Valdez, the estimated median WTP is equal to exp(α) = 41.55. This value is very close to the upper bound provided by the interval of the median WTP in the Range yes model, i.e. 44.21. The discrete choice format is then likely to overestimate means or medians compared to other surveys' formats. It confirms previous research showing that, with the same underlying assumptions, the discrete choice format leads to a systematically higher estimated mean WTP than the openended format [START_REF] Green | Referendum contingent valuation, anchoring, and willingness to pay for public goods[END_REF] or the payment card format [START_REF] Ready | How do respondents with uncertain willingness to pay answer contingent valuation questions?[END_REF].

3. Existing results suggest that anomalies occur in ascending sequences only (i.e. after a yes to the initial bid).7 DeShazo ( 2002) offers a prospect-theory explanation, interpreting the first bid as playing the role of a reference point. The Range model offers an alternative explanation: anomalies come from the fact that, when uncertain, respondents tend to answer yes. Indeed, if the bid belongs to his range of acceptable values, a respondent answers yes to the first question and necessarily no to the second question (see Section 2). This specific behavior occurs in ascending sequences only. Such asymmetry can be viewed from the estimation of the model too, since the Range model can be estimated as a model with two different shift parameters in ascending/descending sequences (see Section 3.1).

All in all, based on Exxon Valdez data, the Range model: (1) confirms existing findings on the effect of respondent uncertainty; (2) offers an alternative explanation to anomalies in CV surveys.

Conclusion

In this article, we develop a model that allows us to deal with respondent uncertainty and starting-point bias in the same framework. This model is based on the principle of coherent arbitrariness, put forward by Ariely et al. (2003b). It allows for respondent uncertainty without having to rely on follow-up questions explicitly designed to measure the degree of that uncertainty (e.g., "How certain are you of your response?"). It provides an alternative interpretation of the fact the some of the responses to the second bid may be inconsistent with the responses to the first bid. This anomaly is explained by respondents' uncertainty, rather than anomalies in respondent behavior. Using the well-known Exxon Valdez survey, our empirical results suggest that, when uncertain, respondents tend to answer yes.

Table 1 :

 1 Exxon Valdez Oil Spill Survey: Random-effect models

	Parameter Single	Double	Shift	M	Range yes
			(δ 1 = δ 2 = 0) (δ 1 = δ 2 )	(n.c.)	(δ 2 = 0)
	α	3.727	3.080	3.754	3.797	3.789
		(0.124)	(0.145)	(0.127)	(0.129)	(0.134)
	σ	3.149	3.594	3.236	3.298	3.459
		(0.432)	(0.493)	(0.421)	(0.387)	(0.272)
	δ 1			-1.108	-1.424	-1.583
				(0.212)	(0.356)	(0.222)
	δ 2				-0.062
					(0.114)
	ρ		0.694	0.770	0.997	0.998
			(0.047)	(0.045)	(0.010)	(0.014)
	ℓ	-695.51

It would be interesting to consider a model in which δ varies across individuals. Some variables that are proved to play a role in individual value assessment (such as repeated exposure to the good or representation of the good(Flachaire and Hollard

2007)) may also influence the length of the range. This requires a particular treatment which is beyond the scope of this paper.

P (yes) = P (yes|b 1i < W i )P (b 1i < W i ) + P (yes|W i < b 1i < W i )P (W i < b 1i < W i ) + P (yes|b 1i > W i )P (b 1i > W i )where the conditional probabilities are respectively equal to 1, ξ and 0.

The bid values are given inAlberini, Kanninen, and Carson (1997, Table 1).

A LR test is equal to twice the difference between the maximized value of the loglikelihood functions (given in the last line ℓ); it is asymptotically distributed as a Chi-squared distribution.

Estimation results of the Range and of the Range yes models obtained by using the constraint ρ = 1 are not reported: they are similar to those obtained without imposing this constraint and the estimates of the loglikelihood functions are identical.

[START_REF] Cameron | Estimation using contingent valuation data from a dichotomous choice with follow-up questionnaire[END_REF][START_REF] Kanninen | Bias in discrete response contingent valuation[END_REF][START_REF] Herriges | Starting point bias in dichotomous choice valuation with follow-up questioning[END_REF][START_REF] Alberini | Modeling response incentive effects in dichotomous choice valuation data[END_REF][START_REF] Whitehead | Incentive incompatibility and starting-point bias in iterative valuation questions[END_REF]

[START_REF] Deshazo | Designing transactions without framing effects in iterative question formats[END_REF][START_REF] Cooper | One and one-half bids for contingent valuation[END_REF][START_REF] Flachaire | Controlling starting-point bias in double-bounded contingent valuation surveys[END_REF]


Hervé Zénouda
email: zenouda@univ-tln.fr

NEW MUSICAL ORGANOLOGY: THE AUDIO GAMES THE QUESTION OF "A-MUSICOLOGICAL" INTERFACES

Keywords: Audio-games, video games, computer generated music, gameplay, interactivity, synesthesia, sound interfaces, relationships image/sound, audiovisual music

This article aims to shed light on a new and emerging creative field: "Audio Games," a crossroad between video games and computer music. Today, a plethora of tiny applications, which propose entertaining audio-visual experiences with a preponderant sound dimension, are available for game consoles, computers, and mobile phones. These experiences represent a new universe where the gameplay of video games is applied to musical composition, hence creating new links between these two fields. In proposing to manipulate what we refer to as "a-musicological" 1 representations (i.e. using symbols not normally associated with traditional musicology to manipulate and produce sound), this creative aspect raises new questions about representations of sound and musical structures and requires new instrumental gestures and approaches to composing music which will be examined. Furthermore, these objects play a role in the rise of a new amateur profile, already put forth by authors like Vilèm Flusser (Flusser, 1996), with regards to photography.

After having defined the characteristics and the limits of this field and highlighting a few of the historical milestones (abstract cinema, gaming theory in music, graphic actions and scores), we will study a few examples of musical games and propose areas for further research to devise analytical tools for these new objects.

1/ Introduction

In this article, we would like to shed some light on an emerging creative field : "Audio Games," a crossroad between video games and computer music. Today, a plethora of tiny applications, which propose entertaining audio-visual experiences with a preponderant sound dimension, are available not only for game consoles and computers, but mobile phones as well. These experiences represent a new universe where the notion of gameplay derived from video games can facilitate the link with musical composition. In proposing to manipulate what we refer to as "a-musicological"2 representations (i.e. using symbols not normally associated with traditional musicology to manipulate and produce sound), this creative aspect raises new questions about representations of sound and musical structures and requires new instrumental gestures and approaches to composing music which will be examined. In an original way, he thus questions the issue of usability with respect to creativity. Indeed, a new organology is emerging, profoundly renewing musical relationships (abstract synesthesiatic representations, 3D manipulations, simulation of physical events like rebounds or elasticity…). After having defined the characteristics and the limits of this field and highlighting a few of the historical milestones (abstract cinema, gaming theory in music, graphic actions and scores), we will study a few examples of musical games and propose areas for further research to devise analytical tools for these new objects.

2/ Definition

A quick search on the Internet gives us many terms describing this new field and its multiple sub-genders : audio-games, music video-games, music memory-games, rhythm-games, pitch-games, volume-games, eidetic music-games, generative music-games… To avoid contention, we prefer to accept the broadest of terms which takes into account all of the situations where games and musical production are combined with the main particularity of the field being the layering of these two universes with points of contact, but also different cognitive objectives. Thus, it is useful to set aside, from the outset, any and all ambiguity by specifying that the object of our research does not directly deal with the field of sound in video games (a field which deals primarily with interactive sound design), but rather a new organology which uses fun video activities to produce sound and extensively uses digital interactivity, creating a new relationship with images. The « audio game », with respect to the dimension of sound, is rooted in a realm between a musical instrument, a music box, and musical automatons. Moreover, the question of balance between the freedoms and constraints of players is crucial to the success of a entertaining sound-based video. Therefore, the richer and more complex the rules are, the more musically interesting the game is, even if it requires a lot of time to learn how to use. On the contrary, the more the constraints are preset, the easier it is for the user to use, managing almost immediately, but with the undeniable risk of producing either mediocre or repetitive sound. A second important characteristic of this new cultural object that we are trying to define is the development of a new relation between image and sound. Indeed, the overlapping of two universes (games and sound production) is materializing in the interface and interactive manipulation which often do not refer to musicology, but rather to rules specific to games (fighting opponents, manipulating objects…). It is above all, and in this case, the use of interfaces that we refer to as "amusicological", as does Francis Rousseau and Alain Bonardi, which appear to be the main originality of this new organology.

3/ Gameplay and Instrumental games

A link exists between video games and sound in the notion of "playing", a notion which deserves our attention. In the world of video games, the terms playability and gameplay are the most often used to describe this dimension. For some (and in Canada in particular), the two terms are considered as synonyms and "jouabilité" is used as the French Translation of "game-play". For others, the two terms refer to different realities, despite being very closely related. The first is considered as a subgroup of the second. The first term refers to the pleasure of playing while the second term represents the principles of the game. Both notions being similar (and each directly depending on the other), we prefer to use the French term of "jouabilité" to describe all of the elements in the ludic video experience: the rules, interface, and maneuverability as well as player appropriation (the pleasure procured and the ease of appropriation). What does the playability of video games and instrumental games have in common? If we define playability as the characteristic of that which is playable, which can be played, we can therefore find a musical link in the notion of musicality, that which is "well composed" for a given instrument and which "sounds" good. We can then speak of "playability" for a piano score in reference to the pleasure procured by the pianist when playing this composition and his or her ability to incorporate, personify, express his or her interpretation. As regards the aspect of applying the rules of the game, there is no direct equivalent of the player that can be found in the traditional roles associated with music : neither a true composer, nor solely an instrumentalist, nor simple listener. Yet, one composer has remarkably shifted how these roles were assigned and enabled the development of a ludic dimension. Indeed, by the end of the 1950s, John Cage (1912-1992) made headway in his research on chance and indetermination by transforming the score into a game with rules that the musician had to incorporate and above all personalize. The score thus changed from notations of musical parameters to that of actions. For example, in "Variations I" (1958), "Variations II" (1961) or "Cartridge Music" (1960), the notes were written as relative values (the size of the points reflect the intensity and length) on transparent sheets the musician placed over other transparent sheets containing the rules of the game (geometric shapes, a clock face…). The overlapping of sheets containing information on different levels (notes and rules) produces a score which must be interpreted. As shown below, the musician must implement a plan to produce the musical information before playing a single note, a "task" normally reserved for composers themselves. This new role of instrumentalists embodies the two English terms which describe games: "game" and "play". The term "game" refers to the notion of structure (a system of rules which the player must respect to successfully carry out an action), while the term "play" denotes a ludic attitude the player adopts ("actions of the player") (Genvo, 2002). In modifying the role of the musician, John Cage considerably increased the amount of freedom and creativity of the musician, two fundamental elements of a ludic attitude. The link between composition and the theory of games can be more explicitly found in the famous performance "Reunion" (1968), featuring Marcel Duchamp playing a game of chess where each move produces musical events more or less randomly. The game theory can be found among other composers such as Iannis Xenakis ("Duel" (1959), "Stratégie" (1962) and "Linaia Agon" (1972)), Mauricio Kagel ("Match" (1964) inspired by a game of tennis) or John Zorn ("Cobra" (1984)).

If these approaches involve a dialogue between two specialists (the composer and the musician), the ludic video objects are particular in nature in that they mainly address a more general amateur public. This mainstream ludic attitude embodies the work of Vilèm Flusser (Flusser, 1996), on photography, writings which particularly shed light on the particular nature of our research: Flusser in fact defines the camera as a structurally complex toy but functionally simple, enabling you to take pictures without any particular skills, making this activity accessible to a vast amateur public : "The camera is not a tool, but a toy and the photographer is not a worker, but a player: not "homo faber" but "homo ludens". 3 And furthermore: "While the camera is based on complex scientific and technical principles, it is very easy to operate. It's a structurally complex toy, but functionally simple. In that way, it is the contrary of a game of chess, which is structurally simple, but functionally complex: Its rules are simple, but it is very difficult to play chess well. A person who operates a camera can very well take excellent pictures without necessarily having the slightest inclination of the complexity of the processes that take place when he or she pushes the button". 4 This transfer of specialized skills (the photographer or the composer) to an amateur appears to be the founding paradigm of this new class of cultural objects. A paradigm which is part of a broader movement linked to new information technologies. Jean Louis Weissberg (Weissberg, 2001), in his article on the emerging amateur figure clearly shows new intermediary spaces which appear between production and reception, between professionals and amateurs. The author puts forth the notion of graduated skills and highlights the political dimension of these new autonomy improving postures. In transferring this capacity, the user-friendliness of the interfaces is clearly essential. If it facilitates the transfer of skills and endeavors to make complex operations more intuitive, we argue that in the field application of musical composition we are studying, the question of user-friendliness is directly linked to the key issue of the representation of sound and musical structures in its ability to make concrete and visible that which is abstract and sound based.

4/ A few historical milestones

We can comprehend the recent emergence of "audio-games" by linking it to the closing gap between graphic arts and musical arts which arose toward the end of the nineteenth century and experienced rapid growth throughout the twentieth century (Bosseur, 1998). The scale of such historical dynamics exceeding the framework of this article (Zénouda, 2008), we shall very briefly introduce three :

-"Audiovisual music": The expression of audiovisual music progressed in the beginning of the 1940s5 thanks to John Withney6 , who defined the characteristics by studying the question of tempo in relation to specific films (combinations of time and space as well as shape and color). Nevertheless, audiovisual music existed long before, as early as the 1920s, with directors like Oskar Fishinger7 or Len Lye8 and is a part of the circle of influence regarding questions of connections between the arts and synesthesia so dear to abstract painters like Kandinsky or Paul Klee. The will of these directors was to find a specific film language "free" of any narration and forms inspired by novels or plays. In doing so, filmmakers strayed from cinema's primary function of recording reality by favoring to use non figurative forms and searching for construction models for their work in music which is the most abstract of arts. With duration and rhythm as a common denominator, these filmmakers sought to produce "completely" synesthetic works playing with the subtle connections between different senses. In the 1970s, the composer Iannis Xenakis, also interested in the connection between image and audio, proposed a graphic interface for the composition of music dubbed UPIC 10 11 . Thanks to a graphic palette, the composer can draw waveforms and amplitude envelopes and control both the structure of the sound and the general form of the work. More recently, Golan Levin 12 , a researcher at MIT 13 , a series of instruments 14 which closely combined image, sound, and gestures. A developer of graphic palettes to which he adds real-time computer generated sounds, he associates movement parameters, like the direction and speed of movement or the pressure of an electronic pencil, with sound parameters, like timbre, pitch, panning, and with graphic parameters, like color, the thickness of a stroke or direction. For Golan Levin, the notions of interactivity and generativity are closely linked: Images and sound are produced in real time as the result of a user's movement, hence creating a "generative and interactive malleable audiovisual substance". 15 In France, the company Blue Yeti 16 proposes a dual screen musical drawing "Grapholine" system based on the transformation of sound samples (via a standard but also customizable sound database) by granular synthesis and offers a large range of manipulations and relations between image and sound (speed of the stroke, transparency, luminosity, color, pencil pressure…). At the UTC de Compiègne, two students 17 in their final year of computer science studies, proposed a virtual reality application (Immersive Music Painter, 2010) 18 in which the user, with his or her gestures, draws curves of different colors and thinknesses to which sound or melodies of controllable pitch, panning, and volume are associated.

These three fields are a part of the aspects of representing sound and interaction with sound and concerns the specialized experimental cinema audience for the first field, and composers and musicians for the latter fields. "Audio-games" add a ludic dimension to these two aspects and in doing so, the question of the user-friendliness and the user-friendliness of the interface; thus making this type of application available to a larger amateur audience, regardless of their knowledge of music.

5/ Typology of "audio-games"

We aim to develop an extremely simple and general typology that incorporates all types of "audio-games" as well as all types of music produced regardless of the style and level user expertis. In doing so, we concentrate on the question of representation (set or dynamic) of both types of sound : the basic elements (paradigmatic axis) and elements created through manipulations (playability) proposed via games (syntagmatic axis).

-The vertical paradigmatic axis pertains to the representation of basic sound elements that the audiogame provides the player. The graphic representation of this basic element range from the classic sol-fa to graphical creations without any direct link to sound in using abstract representations related to synesthesia (and any type of connection with different sound parameters). Note that the distinction between an elementary sound and one that is created depends on the type of game and interaction proposed. Thus, what is considered as composed in one audio game may be considered as elementary in another. The items on this axis may therefore be modified depending on the audio-game that is studied and placed according to their distance or proximity to the traditional sol-fa.

-

The horizontal syntagmatic axis pertains to the representation of sound objects created through the game's playability. It regards the representations of second level sound creations. These representations may be set and close to classic musical manipulations (representations of repetitions, transposition, reversals…) or dynamic of simulations of physical phenomena like rebounding, explosions, accumulations) or describe the dynamics of "musicological" or "a-musicological" playability. The first can find direct musical analogies (moving around within space, mirroring….) the second have no musical analogy whatsoever and imply arbitrary and ad-hoc relations linked to the diegesis of the game (fighting games…). As for the paradigmatic axis, the items on the syntagmatic axis can be modified depending on the audio-game studied and will be positioned according to their distance or proximity to the traditional sol-fa. -"Aura" (on iPhone and iPad) 19 [2,1]20 , very close to the aesthetics of a work of Oskar Fishinger as "Allegretto" (1936) or Jordan Belson's "Allures" (1961), allows users to create their own melodies over a computer generated musical background. Always in harmony with music in the background, the user can select the notes, timbre and volume using simple colored shapes on the screen. The audio-visual creation process is fluid and uninterrupted. The musical and visual background changes simply by shaking your iPhone. The user produces music and abstract shapes which are presented as an interactive generator of background music (and images) with the touch of a button. An application like "SynthPond"21 (iPhone et iPad) [2,1] allows you to place different shapes on circles of varying diameters. Notes are played when they collide with waves generated by the user or with other nodes. Contrary to "Aura", "SythPond" produces repetitive musical loops making it possible to visually anticipate the output by following the movement of the nodes as they get closer to different junctions. The player can select the pitch, timbre, and tempo of the loops, which thus allows you to produce potentially complex melodies. -"Rez" (Tetsuya Mizuguchi, 2001, Sega)22 and "Child of Eden" (Tetsuya Mizuguchi, 2010, Xbox360)23 [2,4] are more similar to traditional games in that they preserve a significant sound dimension. "Rez" is like a fight in which the musical elements are dynamically created by the player's acts. Each time the player's or enemy's vessel shoots, a sound is produced which adapts in rhythm and in harmony. The game experience is therefore quite original, the ludic mission (to destroy the enemy vessels) is the source of the images and sound that is produced. The arguments of the designer referring to Kandinsky and synaesthesia link this game to those previously mentioned. To increase the quest for synaesthesia, the multiple simultaneous sensations are brought on by the vibration of the joystick when the images and sound synchronise. In the "Child of Eden", Tetsuya Mizuguchi continues to improve playability by generating sound using state of the art technological innovations (HD images, 5.1 surround sound, Kinect motion sensors which enable you to play without a mouse or joystick). Motion detectors enable direct interaction with images as well as new types of interactivity (for example, clapping you hands enables you to change weapons during the game). The visual aesthetics are far more dazzling and psychedelic that in Rez and the ludic mission is to eradicate a virus which jeopardizes the project to recreate a human within Eden (the archive of humanity). Each level corresponds to a step in this archive of humanity and the last stage incorporates the personal contributions of players with pictures of their happiest moments. -"Metris"24 (Mark Havryliv, Terumi Narushima, Java Applet) [2,3] adds a musical creation dimension to the famous game "Tetris". A synthetic bell sound is generated in real time each time a block is moved. When the player moves or rotates blocks the pitch changes. They way in which the blocks fit together produces different chords. All of the different possibilities enable players to produce sophisticated micro-tonal compositions without losing the interest of the original "Tetris" game.

-"Pasy02"25 (iPhone and iPad) [2,2] is laid out as a grid that you can reshape and stretch as much as you would like and which comes back to normal with an elastic effect. These physical modifications influence the pitch, tempo, timbre of the musical loop played by a synthesizer with waveforms (sine, triangles, squares, sawtooth) that can be chosen by the user to produce diverse melodies. The simple application offers an original and live production of sound. -"Elektro-Plankton"26 (Toshio Iwai, Nintendo) is an emblematic game which offers ten different plankton themed interfaces with various musical situations enhanced with ludic graphics. Certain interfaces emphasize the strong link between musical gestures and pictorial gestures. Furthermore, with "Tracys," [3,3], the player draws lines (straight or curved) the plankton follow while playing piano notes in rhythm with the graphic shapes created. Yet, others display a labyrinthine and rhizomic dimension of music (using a complete range of possible notes): with "Luminaria" [3,3], several plankton move around on a grid of nodes and links, each link following the arrows. The player can change the connections between the nodes and hence change the direction the plankton take. In doing so, the player modifies the notes that are played. Others use a device which is close to what could be referred to as a sound installation. The "Hanenbrows" [3,2], for example, are projected on the screen and produce musical notes when they bounce off leaves. In changing the angle of the leaves, the player can influence the melodies that are produced. Each time a leaf is hit, it changes color and the sound it makes. A screen like "Nanocarps" [3,2], uses plankton, each with their own behaviour and direction. A sound is produced when the plankton hit a wave and using the microphone allows the player to reorganize them. In the same way, the application "Volvoice" [3,1] uses a computer microphone to record sounds which can then be modified (pitch, speed, filter) as much as you'd like by simply changing the shape of the plankton on the screen. Finally, the screen "Sun-Animalcule" [3,1] proposes for you to plant plankton anywhere on the screen. The musical note depends on where you plant it. The light produced by a day/night cycle hatches the seeds and produces the corresponding musical note. As the plankton embryos get bigger, their musical behaviour changes. Using the same graphical elements, each of the three productions make use of a particular aspect of music: Legato uses audio mixing of melodic lines on a particular theme in a loop, Cellos aligns different preset melodies, Moon tribe allows you to synchronize rhythmic loops. The structure itself of the interaction is copied or transposed on aspects of music such as harmony, counterpoint, melodic structure, synchronization of rhythms. The graphics possess their own aesthetic coherence and arbitrary sounds. In the same way, each visual and audio mode, possesses its own tempo. The tempo of the graphics and that of the music do not always perfectly overlap. They produce visual and audio temporal loop delays. The gesture does not merge the two modes, but coordinates them. It's the junction, the border between the two worlds. If this relationship leads to sensory fusion, it is only elusive, unambiguous, and subject to interpretation that varies greatly from one user to another. It is not directly a part of the technical process, but rather accomplished in the course of an untimely gesture, as a better user appropriation. It is impossible to say whether our gesture is guided by our interest in producing sound or pleasant visual graphics. We imperceptibly emphasize one or the other, thus combining the three dimensions: visual, audio, and gestural. These examples fit into our typology as follows :

« Aura » [2,1], « SynthPond » [2,1], « Rez » [2,4] , « Child of Eden »[2,4] , « Metris » [2,3], « Pasy02 » [2,2] , « Tracys » [3,3], « Luminaria » [3,3], « Hanenbrows » [3,2], « Nanocarps » [3,2], « Volvoice » [3,1] , « Sun-Animalcule » [3,1], « Flying puppet » [3,4]

7/ Towards an analysis grid for "audio games"

In addition to a classification table of these new objects, we propose some ideas for developing a grid analysis of "audio-games" :

-The Distinction in relations between image and sound: Three modes interact and slide from one to another within the same ludic audio video production. Sound for the overall benefit of images (derived from traditional sound and audiovisual illustrations), images for the overall benefit of sound (derived from computerbased music where images aim to represent and manipulate sound), images and sound of equal importance (more specific to "audio-games" and hypermedia) producing perceptible fusion effects between the two modes.

-The Distinction between sound producing modes: Some sounds are produced by direct intervention of the user. For example, when the user moves the mouse, clicks on or goes over an icon. Other sounds are automatically generated by the system without any user intervention, such as automatic background sounds. Yet others are generated automatically by the system but linked to user intervention, like a particular path in the application or an amount of time spent on an interaction. These different means for producing sound have a tendancy to interfere with each other and lead to a certain degree of confusion. Thus, studying precisely how the author manages the untimely audio mixing of the different layers of sound is essential for a detailed analysis on the relationships between images and sound in an interactive situation.

-Taking graphic/audio/gestural tripthych into account: expressed with the notion of mapping (transcribing information that has been received in one register, the movement or graphic manipulation, into another register such as musical in this case). Several types of mapping can generally be distinguished: the relationship in which one parameter of a field corresponds to the parameter of another (one-to-one), the situation in which the parameter of one field is associated with several parameters of the other (one-to-many), and finally the relationship in which several parameters of one field are associated with one parameter of the other (many-toone). In these multisensory associations, the choice in associating the different parameters of each modality at stake and the manner in which they are associated is essential. Indeed, we note which audio and visual dimensions are affected by the interaction and what perceptible effects they produce. Regarding the sound: the note (pitch, length, intensity), the timbre (envelope, frequency…), the rules of manipulating musical structure, the audio mixing of several tracks, the general parameters like tempo… and to which graphic parameters these are assigned to (color, shape, opacity, sharpness, frame, level of iconicity…). What sensory effects are produced by the multiple combinations of image/sound/ gestures ? -The analysis of different cognitive objectives: "Audio-games" present specific situations where a user's gesture controls and produces images and sound at the same time while taking part in another logic, the game itself (for example, destroying space vessels in "Rez" or placing obstacles to manage how balls rebound in "Elektroplankton"). We have demonstrated this specific situation produces perceptible complex effects where the effects of synchronisation and fusion of images and sound are enhanced by gestures and different cognitive stakes. The main difficulty is associating these two levels (a game and musical production) in a meaningful way (neither a confrontational relationship, nor one that is too distant or anecdotal). Ideally, the ludic layer would give rise to new meaningful instrumental gestures in sound production and ultimately innovate music. To obtain optimal results, the game's rules and missions must therefore clarify the musical structures when played while keeping their impact and coherence as a game. We can be seen here, the difficulty of this desired balance.

-These new objects thus stress the necessity of developing multimodal semiotic approaches of analysis which simultaneously take into account what can be seen and heard as well as gestures. A few tools might help us to make headway :

-In 1961, Abraham Moles [START_REF] Moles | Théorie de l'information et perception esthétique[END_REF] proposed a scale of iconicity with thirteen levels for ranking images according to how closely they resemble the real object they represent. This progressive axis went from the most concrete and figurative representations to the most abstract representations like natural languages or artificial languages (mathematics etc.). This scale of iconicity can be applied to sound by developing two axis: that which goes from concrete to musical and that which goes from recorded to simulated (computer generated sound).

-Inspired by Peirce's sign theory, the composer, François Bayle [START_REF] Bayle | Musique acousmatique : propositions … positions[END_REF] defines three properties of sound linked to the attention of the listener: the "icon" (isomorphic image or im-sound): the object is indicated by all of its characteristics, the "index" (indexed images or di-sound): certain graphic traits denote the object, the "symbol" (a metaphore or me-sound): the image represents the object with associative properties. These three kinds of signs give rise to three levels of hearing: one in which sounds are heard as corresponding to directly identifiable referents of reality (quality : quali-sign) ; one in which the relationship is more abstract, the sound becomes a significant element of something. Specialized listening: Sounds are heard as having been transformed (filtering, transposition, insert…), indications of musical composition (singularity: syn-sign); and finally, one in which the sign is governed by a known law which is independent from the sign itself (rebounds, oscillation…), listening which is oriented towards a sense of organisation, formal law…(stability: legi-sign).

-Conceived by a team of musical researchers in Marseilles, an Unité Sémiotique Temporelle is "a musical segment which, even out of context, possesses a precise temporal signification thanks to its morphological structure" 30 . Nineteen USTs were identified and labelled: A word or a literary expression which most directly describes the manner in which the energy of sound is deployed over time [START_REF] Chute | Par vagues, Qui avance, Qui tourne, Qui veut démarrer, Sans direction par divergence d'information[END_REF] , most often with the help of a "morphological appellation, a qualifier which often refers to something extramusical. 32 This extramusical reference is a first step towards a generalization of these labels to other modalities. In this way, we can emphasize that all of these labels refer to an energetic or spatial movement which naturally connect them to gestures and images.

8/ To conclude: Towards what new instrumental and compositional gestures?

It is currently difficult to foresee new instrumental and compositional gestures resulting from these types of interfaces. Nevertheless, we can note that they are part of a general movement which is creating completely new situations of musical interaction: real-time musical devices are transforming musical gestures by increasing or reshaping them, which results in separating gestures from the sound produced. Professional computer generated sound software 33 more and more frequently add network representations, physical simulations (rebounds, soundclouds…), shapes moving through labyrinths of notes, and ludic approaches to their traditional representations (treble clef and bass clef scores, midi data note grids, player piano music rolls, displayed waveforms…) (Vinet, 1999). « Audio-games » play a role in renewing musical gestures as well as the representation of sound and their musical structures. They make playing and composing music easier for a broad audience regardless of their knowledge in music. They make the musical gestures of musicians on stage more visible and comprehensible. Furthermore, they are likely to make the relationship between audiences and composers more explicit thanks to interactivity.

RECOMMENDED LITTERATURE :

-Cage J. ( 1976

RECOMMENDED WEBSITES :

-http://www.centerforvisualmusic.org/ -Allures : http://www.mediafire.com/?fy920bhvu6q6b1v

Figure 1 :

 1 Figure 1 : John Cage (1960), Cartridge Music

Figure 2 :

 2 Figure 2 : John Cage (1968), Reunion (featuring Marcel Duchamp in Toronto)

Figure 3 :

 3 Figure 3 : Jordan Belson (1961), Allures (http://www.mediafire.com/?fy920bhvu6q6b1v) -Graphic scores: As we have seen above with the score Cartridge Music (John Cage, 1960), the principles of indetermination developed by numerous composers starting in the late 1950s 9 caused us to reconsider the score as a musical communication tool. A new genre appeared as sound and visual arts merged. Composers broadened their range of symbols (colors, shapes, depth, textures…) to express new tones and novel musical processes. These new representations introduced spaces of freedom linked to improvisation and emphasized global musical indications

Figure 4 :

 4 Figure 4 : Cornelius Cardew (1963 -1967), Treatise-Graphic interfaces for musical compositions : In the 1970s, the composer Iannis Xenakis, also interested in the connection between image and audio, proposed a graphic interface for the composition of music dubbed UPIC 10 11 . Thanks to a graphic palette, the composer can draw waveforms and amplitude envelopes and control both the structure of the sound and the general form of the work. More recently, Golan Levin 12 , a researcher at MIT 13 , a series of instruments 14 which closely combined image, sound, and gestures. A developer of graphic palettes to which he adds real-time computer generated sounds, he associates movement parameters, like the direction and speed of movement or the pressure of an electronic pencil, with sound parameters, like timbre, pitch, panning, and with graphic parameters, like color, the thickness of a stroke or direction. For Golan Levin, the notions of interactivity and generativity are closely linked: Images and sound are produced in real time as the result of a user's movement, hence creating a "generative and interactive malleable audiovisual substance".15 In France, the company Blue Yeti 16 proposes a dual screen musical drawing "Grapholine" system based on the transformation of sound samples (via a standard but also customizable sound database) by granular synthesis and offers a large range of manipulations and relations between image and sound (speed of the stroke, transparency, luminosity, color, pencil pressure…). At the UTC de Compiègne, two students 17 in their final year of computer science studies, proposed a virtual reality application (Immersive Music Painter, 2010) 18 in which the user, with his or her gestures, draws curves of different colors and thinknesses to which sound or melodies of controllable pitch, panning, and volume are associated.

Figure 5 :

 5 Figure 5 : Typology of « Audio-games » 6/ A brief presentation of a few "audio-games"-"Aura" (on iPhone and iPad)19 [2,1] 20 , very close to the aesthetics of a work of Oskar Fishinger as "Allegretto" (1936) or Jordan Belson's "Allures" (1961), allows users to create their own melodies over a computer generated musical background. Always in harmony with music in the background, the user can select the notes, timbre and volume using simple colored shapes on the screen. The audio-visual creation process is fluid and uninterrupted. The musical and visual background changes simply by shaking your iPhone. The user produces music and abstract shapes which are presented as an interactive generator of background music (and images) with the touch of a button. An application like "SynthPond" 21 (iPhone et iPad) [2,1] allows you to place different shapes on circles of varying diameters. Notes are played when they collide with waves generated by the user or with other nodes. Contrary to "Aura", "SythPond" produces repetitive musical loops making it possible to visually anticipate the output by following the movement of the nodes as they get closer to different junctions. The player can select the pitch, timbre, and tempo of the loops, which thus allows you to produce potentially complex melodies.

Figure

  Figure 6 : « Aura » Figure 7 : « Synthpond »

Figure 8 :

 8 Figure 8 : « Rez » Figure 9 : « Child of Eden »

Figure

  Figure 10 : « Pasy02 »

Figure 11 :

 11 Figure 11 : « ElectroPlankton » -"Flying puppet" (Nicolas Clauss, painter) 27 [3,4] : Nicolas Clauss' website proposes numerous "interactive screens" where visual aesthetics is clearly figurative, seeking a multi-sensorial experience without any objectives or particular missions. While sound is extremely important, the images never reflect any logical representation of the sound. The two modalities have creative autonomy and produce new sensorial experiences. For example, the triptych Legato, Cellos and Moon tribe uses dancing stick figures. Using the same graphical elements, each of the three productions make use of a particular aspect of music: Legato uses audio mixing of melodic lines on a particular theme in a loop, Cellos aligns different preset melodies, Moon tribe allows you to synchronize rhythmic loops. The structure itself of the interaction is copied or transposed on aspects of music such as harmony, counterpoint, melodic structure, synchronization of rhythms. The graphics possess their own aesthetic coherence and arbitrary sounds. In the same way, each visual and audio mode, possesses its own tempo. The tempo of the graphics and that of the music do not always perfectly overlap. They produce visual and audio temporal loop delays. The gesture does not merge the two modes, but coordinates

Figure 12 :

 12 Figure 12 : « Moon Tribe »

Figure 13 :

 13 Figure 13 : Typology of « Audio-games »

  ), Pour les oiseaux, Belfond. -Bonardi A., Rousseau F. (2003)," Music-ripping " : des pratiques qui provoquent la musicologie, ICHIM 03. -Bosseur J. Y. (1998), Musique et arts graphiques, Interactions au XX ième siècle, Minerve, Paris. -Bosseur J. Y. (2005), Du son au signe, Alternatives, Paris. -Collectif (2004), Jouable. Art, jeu et interactivité Workshop/Colloque, Haute école d'arts appliqués HES, Ecole Nationale des Arts Décoratifs, Ciren, Université Paris 8 -Genève, Centre pour l'image contemporaine. -Flusser V. (1996), Pour une philosophie de la photographie, Circé, Paris. -Genvo S. (2002), « Le game design de jeux vidéo : quels types de narration ? » in « Transmédialité de la narration vidéoludique : quels outils d'analyse ? », Comparaison, Peter Lang, 2002, p.103-112. -Havryliv M. (2005), « Playing with Audio : The Relationship between music and games », Master of arts, University Of Wollongong USA. -Kandinsky V. (1969), Du spirituel dans l'art, et dans la peinture en particulier, Denoël-Gonthier, Paris -Manovitch L. (2001), The language of new media, MIT Press, Cambridge. -Natkin S. (2004), Jeux vidéo et médias du XXIe siècle : quels modèles pour les nouveaux loisirs numériques, Paris, Vuibert. -Stranska L. (2001), Les partitions graphiques dans le contexte de la création musicale Tchèque et Slovaque de la seconde moitié du vingtième siècle, Thèse de Musicologie, Paris IV. -Vinet H. (1999), Concepts d'interfaces graphiques pour la production musicale et sonore in Interfaces homme-machine et création musicale, Hermes, Paris. -Weissberg J.L. (2001), L'amateur, l'émergence d'une nouvelle figure politique, http://multitudes.samizdat.net/L-amateuremergence-d-une-figure -Zénouda H. (2008), Les images et les sons dans les hypermédias artistiques contemporains : de la correspondance à la fusion, L'Harmattan, Paris. fusion, L'Harmattan, Paris.

  10 Unité Polyagogique Informatique du CEMAMu (Centre d'Etudes de Mathématiques et Automatique Musicales) 11 http://www.youtube.com/watch?v=yztoaNakKok 12 http://acg.media.mit.edu/people/golan/ 13 Massachusetts Institute of Technology (USA) 14 « Aurora » (1999), « Floo » (1999), « Yellowtail » (1999), « Loom » (1999), « Warbo » (2000) 15 « an inexhaustible audiovisual substance which is created and manipulated through gestural mark-making » Golan Levin, Painterly Interfaces for Audiovisual Performance, B.S. Art and Design, [LEVIN 1994], p.19. 16 http://www.blueyeti.fr/Grapholine.html 17 Camille Barot and Kevin Carpentier.

18

http://www.utc.fr/imp/

  -Golan Levin : http://acg.media.mit.edu/people/golan/ -Blue Yeti : http://www.blueyeti.fr/Grapholine.html -Aura : http://www.youtube.com/watch?v=rb-9AWP9RXw&feature=related -Synthpond : http://www.youtube.com/watch?v=mN4Rig_A8lc&feature=related -REZ : http://www.youtube.com/watch?v=2a1qsp9hXMw -Child Of Eden : http://www.youtube.com/watch?v=xuYWLYjOa_0&feature=fvst -Trope : http://www.youtube.com/watch?v=dlgV0X_GMPw -Pasy02 : http://www.youtube.com/watch?v=JmqdvxLpj6g&feature=related -Sonic Wire : http://www.youtube.com/watch?v=ji4VHWTk8TQ&feature=related -Electroplankton : http://www.youtube.com/watch?v=aPkPGcANAIg -Audio table : http://www.youtube.com/watch?v=vHvH-nWH3QM -Nicolas Clauss : http://www.flyingpuppet.com -Cubase : http://www.steinberg.fr/fr/produits/cubase/start.html -Nodal : http://www.csse.monash.edu.au/~cema/nodal/

We borrow the term « a-musicological» from Francis Rousseau and Alain Bonardi (Bonardi, Rousseau,

2003).

We borrow the term « a-musicological» from Francis Rousseau and Alain Bonardi(Bonardi, Rousseau, 2003).

Referenced above (p.35)

Referenced above (p.78)

Five film exercices (1943 -1944) (http://www.my-os.net/blog/index.php?2006/06/20/330-john-whitney)

Withney J. (1980), Digital harmony on the complementary of music and visual arts, Bytes Books, New Hampshire.

« Studie Nr 7. Poème visuel » (1929-1930), « Studie Nr

» (1931) … 8 « A Colour Box » (1935) …

John Cage but also Earle Brown, Pierre Boulez, André Boucourechliev among others….

http://www.youtube.com/watch?v=rb-9AWP9RXw&feature=related

[2,1] = 2 on the paradigmatic axis and 1 on the syntagmatic axis

http://www.youtube.com/watch?v=mN4Rig_A8lc&feature=related

http://www.youtube.com/watch?v=2a1qsp9hXMw

http://www.youtube.com/watch?v=xuYWLYjOa_0&feature=fvst

Havryliv Mark, Narushima Terumi, « Metris: a game environment for music performance », http://ro.uow.edu.au/era/313/

http://www.youtube.com/watch?v=JmqdvxLpj6g&feature=related

http://www.youtube.com/watch?v=aPkPGcANAIg

http://www.flyingpuppet.com/