11,469 research outputs found
On the Distortion of Voting with Multiple Representative Candidates
We study positional voting rules when candidates and voters are embedded in a
common metric space, and cardinal preferences are naturally given by distances
in the metric space. In a positional voting rule, each candidate receives a
score from each ballot based on the ballot's rank order; the candidate with the
highest total score wins the election. The cost of a candidate is his sum of
distances to all voters, and the distortion of an election is the ratio between
the cost of the elected candidate and the cost of the optimum candidate. We
consider the case when candidates are representative of the population, in the
sense that they are drawn i.i.d. from the population of the voters, and analyze
the expected distortion of positional voting rules.
Our main result is a clean and tight characterization of positional voting
rules that have constant expected distortion (independent of the number of
candidates and the metric space). Our characterization result immediately
implies constant expected distortion for Borda Count and elections in which
each voter approves a constant fraction of all candidates. On the other hand,
we obtain super-constant expected distortion for Plurality, Veto, and approving
a constant number of candidates. These results contrast with previous results
on voting with metric preferences: When the candidates are chosen
adversarially, all of the preceding voting rules have distortion linear in the
number of candidates or voters. Thus, the model of representative candidates
allows us to distinguish voting rules which seem equally bad in the worst case
Utilitarian Collective Choice and Voting
In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result.
Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting.
A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences.
The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior
Comparing Election Methods Where Each Voter Ranks Only Few Candidates
Election rules are formal processes that aggregate voters preferences,
typically to select a single candidate, called the winner. Most of the election
rules studied in the literature require the voters to rank the candidates from
the most to the least preferred one. This method of eliciting preferences is
impractical when the number of candidates to be ranked is large. We ask how
well certain election rules (focusing on positional scoring rules and the
Minimax rule) can be approximated from partial preferences collected through
one of the following procedures: (i) randomized-we ask each voter to rank a
random subset of candidates, and (ii) deterministic-we ask each voter to
provide a ranking of her most preferred candidates (the -truncated
ballot). We establish theoretical bounds on the approximation ratios and we
complement our theoretical analysis with computer simulations. We find that
mostly (apart from the cases when the preferences have no or very little
structure) it is better to use the randomized approach. While we obtain fairly
good approximation guarantees for the Borda rule already for , for
approximating the Minimax rule one needs to ask each voter to compare a larger
set of candidates in order to obtain good guarantees
The Case for Utilitarian Voting
Utilitarian voting (UV) is defined in this paper as any voting rule that allows the voter to rank all of the alternatives by means of the scores permitted under a given voting scale. Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores -1, 0, 1.
The paper deals extensively with Arrow’s impossibility theorem that has been interpreted as precluding a satisfactory voting mechanism. I challenge the relevance of the ordinal framework in which that theorem is expressed and argue that instead utilitarian, i.e. cardinal social choice theory is relevant for voting. I show that justifications of both utilitarian social choice and of majority rule can be modified to derive UV. The most elementary derivation of UV is based on the view that no justification exists for restricting voters’ freedom to rank the alternatives on a given scale
On the Distortion Value of the Elections with Abstention
In Spatial Voting Theory, distortion is a measure of how good the winner is.
It is proved that no deterministic voting mechanism can guarantee a distortion
better than , even for simple metrics such as a line. In this study, we wish
to answer the following question: how does the distortion value change if we
allow less motivated agents to abstain from the election?
We consider an election with two candidates and suggest an abstention model,
which is a more general form of the abstention model proposed by Kirchgassner.
We define the concepts of the expected winner and the expected distortion to
evaluate the distortion of an election in our model. Our results fully
characterize the distortion value and provide a rather complete picture of the
model.Comment: Revised version of the paper appeared in AAAI-1
Utilitarian Collective Choice and Voting
In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior.approval voting ; cardinal collective choice ; evaluative voting ; strategic voting ; voting paradoxes
The Case for Utilitarian Voting
Utilitarian voting (UV) is defined in this paper as any voting rule that allows the voter to rank all of the alternatives by means of the scores permitted under a given voting scale. Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores -1, 0, 1. The paper deals extensively with Arrow’s impossibility theorem that has been interpreted as precluding a satisfactory voting mechanism. I challenge the relevance of the ordinal framework in which that theorem is expressed and argue that instead utilitarian, i.e. cardinal social choice theory is relevant for voting. I show that justifications of both utilitarian social choice and of majority rule can be modified to derive UV. The most elementary derivation of UV is based on the view that no justification exists for restricting voters’ freedom to rank the alternatives on a given scale.approval voting;Arrow’s impossibility theorem ; cardinal collective choice ; evaluative voting ; majority rule ; range voting ; utilitarian voting
A Framework for Approval-based Budgeting Methods
We define and study a general framework for approval-based budgeting methods
and compare certain methods within this framework by their axiomatic and
computational properties. Furthermore, we visualize their behavior on certain
Euclidean distributions and analyze them experimentally
Referendum Design, Quorum Rules and Turnout
In this article, we focus on the consequences of quorum requirements for turnout in referendums. We use a rational choice, decision theoretic voting model to demonstrate that participation quorums change the incentives some electors face, inducing those who oppose changes in the status quo and expect to be in the minority to abstain. As a result, paradoxically, participation quorums decrease electoral participation. We test our model’s predictions using data for all referendums held in current European Union countries from 1970 until 2007, and show that the existence of a participation quorums increases abstention by more than ten percentage points.Referendum Design; Voter turnout
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