Sincerity and manipulation under approval voting

Under approval voting, each voter can nominate as many candidates as she wishes and the election winners are those candidates that are nominated most often. A voter is said to have voted sincerely if she prefers all those candidates she nominated to all other candidates. As there can be a set of winning candidates rather than just a single winner, a voter’s incentives to vote sincerely will depend on what assumptions we are willing to make regarding the principles by which voters extend their preferences over individual candidates to preferences over sets of candidates. We formulate two such principles, replacement and deletion, and we show that, under approval voting, a voter who accepts those two principles and who knows how the other voters will vote will never have an incentive to vote insincerely. We then discuss the consequences of this result for a number of standard principles of preference extension in view of sincere voting under approval voting.     

Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser

Theory and Decision - Under approval voting (AV), each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The preference approval voting (PAV) is a hybrid...     

Sequential voting by veto: Making the Mueller-Moulin algorithm more versatile

This paper shows that a relatively easy algorithm for computing the (unique) outcome of a sophisticated voting procedure called sequential voting by veto (SVV) applies to a more general situation than considered hitherto. According to this procedure a sequence of n voters must select s out of m + s options (s > 0, m 3 n 3 2). The ith voter, when his turn comes, vetoes k _i options (k _i 1, k _i = m). The s remaining non-vetoed options are selected. Every voter is assumed to be fully informed of all other voters total (linear) preference orderings among the competing options, as well as of the order in which the veto votes are cast. This algorithm was proposed by Mueller (1978) for the special case where s and the k _i are all equal to 1, and extended by Moulin (1983) to the somewhat more general case where the k _i are arbitrary but s is still 1. Some theoretical and practical issues of voting by veto are discussed.     

Rank-dominant strategy and sincere voting

Theory and Decision - This study considers a voting rule wherein each player sincerely votes when he/she has no information about the preferences of the other players. We introduce the concept of...     

Positionalist voting functions

Positionalist voting functions are those social choice functions where the positions of the alternatives in the voter's preference orders crucially influence the social ordering of the alternatives. An important subclass consists of those voting functions where numbers are assigned to the alternatives in the preference orders and the social ordering is computed from these numbers. Such voting functions are called representable. Various well-known conditions for voting functions are introduced and it is investigated which representable voting functions satisfy these conditions. It is shown that no representable voting function satisfies the Condorcet criterion. This condition and Arrow's independence condition, which are typical non-positionalist conditions, are shown to be incompatible. The Borda function, which is a well-known positionalist voting function, is studied extensively, conditions uniquely characterizing it are given and some modifications of the function are investigated.My thanks are due to professor Bengt Hansson for encouragement and several helpful suggestions.     

The Pareto rule and strategic voting

This paper uses a particular choice rule over sets of alternatives under the Pareto rule. Starting from the sincere situation every strategic misrevelation of preference is shown to be an improvement for all voters. The existence of an equilibrium under successive misrepresentations by sincere voters is demonstrated.     

Majority voting on orders

We characterize two lexicographic-type preference extension rules from a set X to the set of all orders on this set. Elements of X are interpreted as basic economic policy decisions, whereas elements of are conceived as political programs among which a collectivity has to choose through majority voting. The main axiom is called tournament-consistency, and states that whenever majority pairwise comparisons based on initial preferences on X define an order on X, then this order is also chosen by a majority among all other orders in . Tournament-consistency thus allows to predict the outcome of majority voting upon orders from the knowledge of majority preferences on their components.     

Communication compatible voting rules

We reassess the possibility of full information pooling in a Condorcet jury environment featuring heterogeneous and privately known preference types. We find that in general, with uncorrelated preference types, only very limited heterogeneity is compatible with full pooling. We provide a sufficient condition, based on a simple measure of preference misalignment, under which the set of voting rules compatible with full pooling is at most a singleton. As a caveat to any simplistic conclusions, we identify a case in which an increase in heterogeneity (i.e. polarization) systematically generates the possibility of full pooling. Increased jury size, in contrast, is shown to always render full pooling more difficult.     

A procedural model of voting

The formal framework of social choice theory is generalized through the introduction of separate representations of preferences and choices. This makes it possible to treat voting as a procedure in which decisions are actually made by interacting participants, rather than as a mere mechanism for aggregation. The extended framework also allows for non-consequentialist preferences that take procedural factors into account. Concepts such as decisiveness, anonymity, neutrality, and stability are redefined for use in the new context. The formal results obtained confirm the universality of strategic voting.     

Presidential voting in the west

Voters in the western United States are becoming more Republican than the rest of the country in their presidential choices. The Solid West has replaced the Solid South as a reality of presidential campaigns. This is in spite of a long term national trend away from strong party loyalties. This article examines the ten states of the Interior West at the county level during the eight presidential elections from 1956 through 1984. All parts of the region did not simultaneously embrace the Republican Party from the onset of the New Western Normal Vote episode. Those areas that lagged were characterized by sizable employment in forestry and mining, large Hispanic or Native American populations, or were among the region's few large urban concentrations. Some of these areas still remain outside the Republican fold in presidential elections. The overall magnitude of change in Republicanism in the 549 counties was not uniform, but rather impacted some areas such as Nevada and Idaho to a much larger degree than others such as Montana and the Dakotas. This article generally confirms Archer and Taylor's assertion that the Western Periphery constitutes a new Republican heartland. But some Indian and Hispanic populations continue to vote for Democratic presidential candidates. Rural areas with strong organized labor such as the mining and forestry areas of Montana, and big cities like Denver are only weakly Republican. Hence, the conversion to strong and unwaivering Republicanism is not total and may never occur.     

Pareto improvements by Pareto strategic voting under majority voting with risk loving and risk avoiding voters — A note

Voters satisfy maximin or maximax in their choices between sets of alternatives and secure a Pareto improvement by all voting strategically under simple majority voting for particular sincere preferences. Thus the assumption that strategic voting is a bad thing is challenged and the idea that we should reject voting because of the possibility of misrepresentation dismissed.     

Strict proportional power in voting bodies

It is a widely known fact among game theorists as well as political scientists that the distribution of voting weights in a voting body is generally a poor proxy for the distribution of voting power within the body. It has been proposed to equate the distribution of a priori voting power and actual seat distribution by randomizing the decision rule of the voting body over various majority rules. In this paper, some implications of this procedure will be discussed.     

Approval voting and strategy analysis: A Venetian example

The author presents a historic reconstruction of the single-member constituency election system known as approval voting which was used to elect Venetian dogi for over 500 years. An interesting procedure theoretically, concurrent approval voting is the only sincere single-winner election system. Central issues concerning strategy choice under uncertainty are investigated using a contingency-dependent framework of individual behavior given prior probability distributions over decision relevant propositions. Extensions are then proposed for the use of approval procedures in modern elections and other collective decision-making situations. Finally the advantages of trichotomous preferences in decision and strategy analysis are argued.Masculine personal pronouns are used when discussing doge elections, otherwise feminine pronouns are used.     

The uncovered set in spatial voting games

In a majority rule voting game, the uncovered set is the set of alternatives each of which can defeat every other alternative in the space either directly or indirectly at one remove. Research has suggested that outcomes under most reasonable agenda processes (both sincere and sophisticated) will be confined to the uncovered set. Most research on the uncovered set has been done in the context of voting games with a finite number of alternatives and relatively little is known about the properties of the uncovered set in spatial voting games.We examine the geometry of the uncovered set in spatial voting games and the geometry of two important subsets of the uncovered set, the Banks set and the Schattschneider set. In particular, we find both general upper and lower limits on the size of the uncovered set, and we give the exact bounds of the uncovered set for situations with three voters. For situations with three voters, we show that the Banks set is identical to the uncovered set.     

Majority efficiencies for simple voting procedures: Summary and interpretation

Several studies published during the past five years have attempted to assess the propensities of different voting procedures to elect the simple majority candidate when one exists in a multicandidate election. The present paper provides a summary of what we believe to be the most salient results of this research. The data are first discussed within the context of the assumptions used in our simulations. We then extend our interpretations to account for potential political realities that were not incorporated in the simulations.     

Ordinal equivalence of power notions in voting games

In this paper, we are concerned with the preorderings (SS) and (BC) induced in the set of players of a simple game by the Shapley–Shubik and the Banzhaf–Coleman's indices, respectively. Our main result is a generalization of Tomiyama's 1987 result on ordinal power equivalence in simple games; more precisely, we obtain a characterization of the simple games for which the (SS) and the (BC) preorderings coincide with the desirability preordering (T), a concept introduced by Isbell (1958), and recently reconsidered by Taylor (1995): this happens if and only if the game is swap robust, a concept introduced by Taylor and Zwicker (1993). Since any weighted majority game is swap robust, our result is therefore a generalization of Tomiyama's. Other results obtained in this paper say that the desirability relation keeps itself in all the veto-holder extensions of any simple game, and so does the (SS) preordering in all the veto-holder extensions of any swap robust simple game.     

Strategic voting in the 1984 democratic presidential primaries

When casting their ballots in primary elections, voters usually vote in a straight-forward manner for the candidate of their preference. But sometimes sophisticated voters vote for a second or third choice who has a better chance of winning in the general election or even cross over to the opposition party to vote for a candidate who will be easier to defeat in the general election. This article assesses the amount and importance of such strategic voting in Democratic presidential primaries in 1984 using discriminate analysis.     

A note on manipulability of large voting schemes

A voting system is a rule which assigns to every possible combination of votes (by any number of individuals) an alternative. We define the notion of asymptotic nonmanipulability for voting systems, and prove that every representable positionalist voting system is asymptotically nonmanipulable. Various aspects of manipulation of large voting schemes and several examples are also discussed.