Parliamentary voting rules and strategic candidacy

In this paper we study the vulnerability of parliamentary voting procedures to strategic candidacy. Candidates involved in an election are susceptible to influence the outcome by opting out or opting in. In the context of three-alternative elections and under the impartial anonymous culture assumption, we evaluate the frequencies of such strategic candidacy opportunities.strategic candidacy, parliamentary voting procedures, opting out, opting in, impartial anonymous culture.

Axiomatizations for the Shapley-Shubik power index for games with several levels of approval in the input and output

The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in the input and the output. The corresponding games are called $(j,k)$ simple games. Here we present a new axiomatization for the Shapley-Shubik index for $(j,k)$ simple games as well as for a continuous variant, which may be considered as the limit case.Comment: 25 page

An Axiomatization of the Shapley-Shubik Index for Interval Decisions

The Shapley-Shubik index was designed to evaluate the power distribution in committee systems drawing binary decisions and is one of the most established power indices. It was generalized to decisions with more than two levels of approval in the input and output. In the limit we have a continuum of options. For these games with interval decisions we prove an axiomatization of a power measure and show that the Shapley-Shubik index for simple games, as well as for $(j,k)$ simple games, occurs as a special discretization. This relation and the closeness of the stated axiomatization to the classical case suggests to speak of the Shapley-Shubik index for games with interval decisions, that can also be generalized to a value.Comment: 28 pages, 3 figure

Fraudulent Democracy: A Dynamic Ordinal Game Approach

We propose a model of political competition and stability in nominally democratic societies characterized by fraudulent elections. In each election, an opposition leader is pitted against the leader in power. If the latter wins, he remains in power, which automatically makes him the incumbent candidate in the next election as there are no term limits. If he loses, there is an exogenously positive probability that he will steal the election. We model voter forward-looking behavior, defining a new solution concept. We then examine the existence, popularity, and welfare properties of equilibrium leaders, these being leaders who would remain in power indefinitely without stealing elections. We find that equilibrium leaders always exist. However, they are generally unpopular, and may be inefficient. We identify three types of conditions under which equilibrium leaders are efficient. First, efficiency is achieved under any constitutional arrangement if and only if there are at most four competing leaders. Second, when there are more than four competing leaders, efficiency is achieved if and only if the prevailing political system is an oligarchy, which means that political power rests with a unique minimal coalition. Third, for a very large class of preferences that strictly includes the class of single-peaked preferences, equilibrium leaders are always efficient and popular regardless of the level of political competition. The analysis implies that an excessive number of competing politicians, perhaps due to a high level of ethnic fragmentation, may lead to political failure by favoring the emergence of a ruling leader who is able to persist in power forever without stealing elections, despite being inefficient and unpopular

The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis

The fact that voters can manipulate election outcomes by misrepresenting their true preferences over competing political parties or candidates is commonly viewed as a major flaw of democratic voting systems. It is argued that insincere voting typically leads to suboptimal voting outcomes. However, it is also understood that insincere voting is rational behavior as it may result in the election of a candidate preferred by the voter to the candidate who would otherwise be selected. The relative magnitude of the welfare gains and losses of those who benefit from and those adversely affected by insincere voting behavior is consequently an important empirical issue. We address this question by providing exact asymptotic bounds on the welfare effects, in equilibrium, of insincere voting for an infinite class of democratic rules. We find, for instance, that preference manipulation benefits one-half to two-thirds of the population in three-candidate elections held under first-past-the-post, and one-third to one-hundred percent of the population in antiplurality elections. These bounds differ from those obtained under out-of-equilibrium manipulation. Our partial identification analysis provides a novel approach to evaluating mechanisms as a function of attitude towards risk, and it has practical implications for the choice of election rules by a mechanism designer facing a worst-case or a best-case objective. It also provides a new answer to the longstanding question of why certain rules, such as first-past-the-post, are more common in practice

Fraudulent Democracy: A Dynamic Ordinal Game Approach

We propose a model of political competition and stability in nominally democratic societies characterized by fraudulent elections. In each election, an opposition leader is pitted against the leader in power. If the latter wins, he remains in power, which automatically makes him the incumbent candidate in the next election as there are no term limits. If he loses, there is an exogenously positive probability that he will steal the election. We model voter forward-looking behavior, defining a new solution concept. We then examine the existence, popularity, and welfare properties of equilibrium leaders, these being leaders who would remain in power indefinitely without stealing elections. We find that equilibrium leaders always exist. However, they are generally unpopular, and may be inefficient. We identify three types of conditions under which equilibrium leaders are efficient. First, efficiency is achieved under any constitutional arrangement if and only if there are at most four competing leaders. Second, when there are more than four competing leaders, efficiency is achieved if and only if the prevailing political system is an oligarchy, which means that political power rests with a unique minimal coalition. Third, for a very large class of preferences that strictly includes the class of single-peaked preferences, equilibrium leaders are always efficient and popular regardless of the level of political competition. The analysis implies that an excessive number of competing politicians, perhaps due to a high level of ethnic fragmentation, may lead to political failure by favoring the emergence of a ruling leader who is able to persist in power forever without stealing elections, despite being inefficient and unpopular

The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis

The fact that voters can manipulate election outcomes by misrepresenting their true preferences over competing political parties or candidates is commonly viewed as a major flaw of democratic voting systems. It is argued that insincere voting typically leads to suboptimal voting outcomes. However, it is also understood that insincere voting is rational behavior as it may result in the election of a candidate preferred by the voter to the candidate who would otherwise be selected. The relative magnitude of the welfare gains and losses of those who benefit from and those adversely affected by insincere voting behavior is consequently an important empirical issue. We address this question by providing exact asymptotic bounds on the welfare effects, in equilibrium, of insincere voting for an infinite class of democratic rules. We find, for instance, that preference manipulation benefits one-half to two-thirds of the population in three-candidate elections held under first-past-the-post, and one-third to one-hundred percent of the population in antiplurality elections. These bounds differ from those obtained under out-of-equilibrium manipulation. Our partial identification analysis provides a novel approach to evaluating mechanisms as a function of attitude towards risk, and it has practical implications for the choice of election rules by a mechanism designer facing a worst-case or a best-case objective. It also provides a new answer to the longstanding question of why certain rules, such as first-past-the-post, are more common in practice

“One Man, One Vote” Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May

This paper is dedicated to the measurement of (or lack of) electoral justice in the 2010 Electoral College using a methodology based on the expected influence of the vote of each citizen for three probability models. Our first contribution is to revisit and reproduce the results obtained by Owen (1975) for the 1960 and 1970 Electoral College. His work displays an intriguing coincidence between the conclusions drawn respectively from the Banzhaf and Shapley-Shubik’s probability models. Both probability models conclude to a violation of electoral justice at the expense of small states. Our second contribution is to demonstrate that this conclusion is completely flipped upside-down when we use May’s probability model: this model leads instead to a violation of electoral justice at the expense of large states. Besides unifying disparate approaches through a common measurement methodology, one main lesson of the paper is that the conclusions are sensitive to the probability models which are used and in particular to the type and magnitude of correlation between voters that they carry

Monotonicity paradoxes in three-candidate elections using scoring elimination rules

International audienceScoring elimination rules (SER), that give points to candidates according to their rank in voters’ preference orders and eliminate the candidate(s) with the lowest number of points, constitute an important class of voting rules. This class of rules, that includes some famous voting methods such as Plurality Runoff or Coombs Rule, suffers from a severe pathology known as monotonicity paradox or monotonicity failure, that is, getting more points from voters can make a candidate a loser and getting fewer points can make a candidate a winner. In this paper, we study three-candidate elections and we identify, under various conditions, which SER minimizes the probability that a monotonicity paradox occurs. We also analyze some strategic aspects of these monotonicity failures. The probability model on which our results are based is the impartial anonymous culture condition, often used in this kind of study