An analytical and experimental comparison of maximal lottery schemes

Maximal lottery ($$ ML $$ ML ) schemes constitute an interesting class of randomized voting rules that were proposed by Peter Fishburn in 1984 and have been repeatedly recommended for practical use. However, the subtle differences between different $$ ML $$ ML schemes are often overlooked. Two canonical subsets of $$ ML $$ ML schemes are "Image missing" schemes (which only depend on unweighted majority comparisons) and "Image missing" schemes (which only depend on weighted majority comparisons). We prove that "Image missing" schemes are the only homogeneous $$ ML $$ ML schemes that satisfy $$ SD $$ SD -efficiency and $$ SD $$ SD -participation, but are also among the most manipulable $$ ML $$ ML schemes. While all $$ ML $$ ML schemes are manipulable and even violate monotonicity, they are never manipulable when a Condorcet winner exists and satisfy a relative notion of monotonicity. We also evaluate the frequency of manipulable preference profiles and the degree of randomization of $$ ML $$ ML schemes via extensive computer simulations. In summary, $$ ML $$ ML schemes are rarely manipulable and often do not randomize at all, especially for few alternatives. The average degree of randomization of "Image missing" schemes is consistently lower than that of "Image missing" schemes.

Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?

Using thermometer score data from the ANES, we show that while there may have been no clear-cut Condorcet winner among the 2016 US presidential candidates, there appears to have been a Condorcet loser: Donald Trump. Thus the surprise is that the electorate preferred not only Hillary Clinton, but also the two “minor” candidates, Gary Johnson and Jill Stein, to Trump. Another surprise is that Johnson may have been the Condorcet winner. A minimal normative standard for evaluating voting systems is advanced, privileging those systems that select Condorcet winners if one exists, and critiquing systems that allow the selection of Condorcet losers. A variety of voting mechanisms are evaluated using the 2016 thermometer scores: Condorcet voting, plurality, Borda, (single winner) Hare, Coombs, range voting, and approval voting. We conclude that the essential problem with the existing voting procedure—Electoral College runoff of primary winners of two major parties—is that it (demonstrably) allows the selection of a Condorcet loser.

The Incidence of Some Voting Paradoxes Under Domain Restrictions

Voting paradoxes have played an important role in the theory of voting. They typically say very little about the circumstances in which they are particularly likely or unlikely to occur. They are basically existence findings. In this article we study some well known voting paradoxes under the assumption that the underlying profiles are drawn from the Condorcet domain, i.e. a set of preference profiles where a Condorcet winner exists. The motivation for this restriction is the often stated assumption that profiles with a Condorcet winner are more likely than those without it. We further restrict the profiles by assuming that the starting point of our analysis is that the Condorcet winner coincides with the choice of the voting rule under scrutiny. The reason for making this additional restriction is that—intuitively—the outcomes that coincide with the Condorcet winner make those outcomes stable and, thus, presumably less vulnerable to various voting paradoxes. It will be seen that this is, indeed, the case for some voting rules and some voting paradoxes, but not for all of them.

Trading Votes for Votes. A Dynamic Theory

We develop a framework to study the dynamics of vote trading over multiple binary issues. We prove that there always exists a stable allocation of votes that is reachable in a finite number of trades, for any number of voters and issues, any separable preference profile, and any restrictions on the coalitions that may form. If at every step all blocking trades are chosen with positive probability, convergence to a stable allocation occurs in finite time with probability 1. If coalitions are unrestricted, the outcome of vote trading must be Pareto optimal, but unless there are three voters or two issues, it need not correspond to the Condorcet winner.

Runoff Amid a Plethora of Political Parties

This chapter explores the impact of runoff in the four nations where the number of parties averaged above 3.75 and coalitions did not emerge for presidential elections. The large number was not problematic in Colombia or Guatemala; levels of democracy improved in both countries as political exclusion of the left diminished. The large number was, however, problematic in Ecuador and, to a lesser degree, Peru. Presidents’ first-round tallies were often very low and at times presidents might not have been the Condorcet winner. Especially when presidents were unpopular, executive-legislative conflict could be severe. The weakness of political parties set the stage for the damages to democracy inflicted by the Serrano, Fujimori, and Bucaram governments. However, although levels of democracy declined in Ecuador amid the large number of parties, they declined more steeply after the election of Correa and a reduction in the number of parties.

Content-Based Agendas and Qualified Majorities in Sequential Voting

We analyze sequential, binary voting schemes in settings where several privately informed agents have single-peaked preferences over a finite set of alternatives, and we focus on robust equilibria that do not depend on assumptions about the players' beliefs about each other. Our main results identify two intuitive conditions on binary voting trees, ensuring that sincere voting at each stage forms an ex post perfect equilibrium. In particular, we uncover a strong rationale for content-based agendas: if the outcome should not be sensitive to beliefs about others, nor to the deployment of strategic skills, the agenda needs to be built “from the extremes to the middle” so that more extreme alternatives are both more difficult to adopt, and are put to vote before other, more moderate options. An important corollary is that, under simple majority, the equilibrium outcome of the incomplete information game is always the Condorcet winner. Finally, we aim to guide the practical design of schemes that are widely used by legislatures and committees and we illustrate our findings with several case studies. (JEL D71, D72, I10, J16, J32, K10)

Selection of subcontractors using ordinal ranking methods based on Condorcet approach

A choice of a subcontractor may have critical impact on realization of the project, it has influence on the cost, duration, and quality. Selection of the best sucontractor can be defined as multiple criteria decision making problem (MCDM) of choosing a proper offer from set of alternatives evaluated by using set of criteria. Decision maker should determine the criteria as objective and measurable. Significance of decision making problem is presented by large amount of theories and methods developed for solving MCDM problems and number of criteria considered in these problems. A Condorcet method (formulated over two centuries ago) is commonly accepted for democratic (majority of criteria determines the winner) and fair election – a Condorcet winner is the alternative which is preferred in all pair-wise comparisons. According to social choice theory where a Condorcet winner cannot be obtained from a set of alternatives, the best solution is close to being a Condorcet winner. The paper presents four selection methods of the best alternative that is as close as possible to being a Condorcet winner and contains examples of a subcontractor selection using only ordinal scales of evaluation of alternatives.