Michel Truchon

On reforming the welfare system: Workfare meets the negative income tax

Abstract Using a simulation model for a small open economy (Quebec 1986), various Negative Income Tax (NIT) and workfare schemes are compared from the point of view of efficiency and equity. The main finding is that there exist workfare schemes that are superior both to the Quebec regime of 1986, and to a NIT characterized by a 100 percent implicit tax rate. However, these workfare schemes are dominated by some NIT programs. This suggests that it may be necessary to have work requirements that vary across socio-demographic classes for a workfare plan to be superior to any NIT. Combining workfare with an NIT could also be the prescription.

Maximum likelihood approach to vote aggregation with variable probabilities

Abstract. The Condorcet-Kemeny-Young statistical approach to vote aggregation is based on the assumption that voters have the same probability of comparing correctly two alternatives and that this probability is the same for any pair of alternatives. We relax the second part of this assumption by letting the probability of comparing correctly two alternatives be increasing with the distance between two alternatives in the allegedly true ranking. This leads to a rule in which the majority in favor of one alternative against another one is given a larger weight the larger the distance between the two alternatives in the true ranking, i.e., the larger the probability that the voters compare them correctly. This rule is not Condorcet consistent and does not satisfy local independence of irrelevant alternatives. Yet, it is anonymous, neutral, and paretian. It also appears that its performance in selecting the alternative most likely to be the best improves with the rate at which the probability increases.

Boundary optima and the theory of public goods supply

Abstract This paper derives a generalized optimality condition that is valid for all boundary optima in an economy with many public goods and one private good. This condition is then used to show that there is an open subset of Pareto optima where Samuelsons condition does not hold. Finally, it is shown that allocation and distribution are inextricable at these optima, even under conditions that guarantee independence of allocation and distribution at interior optima.

Aggregation of Rankings in Figure Skating

We scrutinize and compare, from the perspective of modern theory of social choice, two rules that have been used to rank competitors in Figure Skating for the past decades. The first rule has been in use at least from 1982 until 1998, when it was replaced by a new one. We also compare these two rules with the Borda and the Kemeny rules. The four rules are illustrated with examples and with the data of 30 Olympic competitions. The comparisons show that the choice of a rule can have a real impact on the rankings. In these data, we found as many as 19 cycles of the majority relation, involving as many as nine skaters. In this context, the Kemeny rule appears as a natural extension of the Condorcet rule. As a side result, we show that the Copeland rule can be used to partition the skaters in such a way that it suffice to find Kemeny rankings within subsets of the partition that are not singletons and then, to juxtapose these rankings to get a complete Kemeny ranking. We also propose the concept of the mean Kemeny ranking, which when it exists, may obviate the multiplicity of Kemeny rankings. Finally, the fours rules are examined in terms of their manipulability. It appears that the new rule used in Figure Skating may be more difficult to manipulate than the previous one but less so than the Kemeny rule.

Voting games and acyclic collective choice rules

Abstract The subject of this paper is the representation of collective choice rules by voting games and the acyclicity of these rules. A collective choice rule is a function that associates a collective preference with every profile of individual preferences. Such a rule is acyclic if it always yields an acyclic collective preference. A voting game is either a simple game or a non-neutral version of such a game called a binary game in constitutional form. Both are special forms of cooperative games that simply specify the structure of power in a society or an organization. The power structure conferred by certain collective choice rules takes the form of a voting game. The paper classifies collective choice rules that can or cannot be represented by a voting game. Conditions for the acyclicity of the collective choice rules that can be represented by a voting game are then obtained from the structure of their corresponding voting games. These results are applied to a large class of voting rules defined by quotas.

Social choice, optimal inference and figure skating

We approach the social choice problem as one of optimal statistical inference. If individual voters or judges observe the true order on a set of alternatives with error, then it is possible to use the set of individual rankings to make probability statements about the correct social order. Given the posterior distribution for orders and a suitably chosen loss function, an optimal order is one that minimises expected posterior loss. The paper develops a statistical model describing the behaviour of judges, and discusses Markov chain Monte Carlo estimation. We also discuss criteria for choosing the appropriate loss functions. We apply our methods to a well-known problem: determining the correct ranking for figure skaters competing at the Olympic Games.

Acyclicity and the Dispersion of the Veto Power

Blair and Pollak (Econometrica (1982) 50: 931–943) prove that, if there are more alternatives than individuals, then, for every arrovian binary decision rule that is acyclic, there is at least one individual who has a veto power over a critical number of pairs of alternatives. If the number of individuals is larger than the number of alternatives, there need not be single vetoers but there could be small coalitions endowed with a similar power. Kelsey (Soc Choice Welfare (1985) 2: 131–137) states precise results in this respect. In this paper, we first give a new and much simpler proof of the main result of Blair and Pollak and complete proofs of the generalization of this result by Kelsey. Then we give a precise answer as to the minimum size of the coalitions that must have a veto power under any acyclic binary decision rule and the minimum number of pairs of alternatives on which these coalitions may exercise their power. We also show that, if the veto power of the coalitions of the minimal size attainable under the last objective is limited to the minimum number of pairs of alternatives, then all larger coalitions have a veto power on all pairs. All the results are obtained by appealing to an acyclicity condition found by Ferejohn and Fishburn (J Econ Theory (1979) 21: 28–45). In the case of symmetric and monotonic binary decision rules, proofs are even easier and illustrate clearly the reasons for the veto power.

Statistical comparison of aggregation rules for votes

If individual voters observe the true ranking on a set of alternatives with error, then the social choice problem, that is, the problem of aggregating their observations, is one of statistical inference. This study develops a statistical methodology that can be used to evaluate the properties of a given or aggregation rule. These techniques are then applied to some well-known rules.

Aggregation of Rankings: A Brief Review of Distance-Based Rules

Some researchers have addressed the problem of aggregating individual preferences or rankings by seeking a ranking that is closest to the individual rankings. Their methods differ according to the notion of distance that they use. The best known method of this sort is due to Kemeny. The first part of this paper offers a brief survey of some of these methods. Another way of approaching the aggregation of rankings is as a problem of optimal statistical inference, in which an expected loss is minimised. This approach requires a loss function, a concept closely related the notion of distance between rankings. The second part of this paper examines two classes of parametric functions and proposes one class for the optimal statistical inference problem.

On the Importance of Lags in Growth Models

This paper is mainly a study of the importance of lags in growth models of the von Neumann type. Lags considered are of two kinds. There are first, the lags in the formation of capital and second, the lags in satisfying the intermediate and final demand. These two kinds of lags slow the expansion of the economy but it is shown that a change in the length of the first kind of lags will not in general have an important effect on the rate of growth of the economy while for the second kind it may have a more drastic effect. The study is made in the framework of a dynamic Leontief model presented by Tsukui. Some calculations are made using his data. A method for handling the second kind of lags is also proposed.