Susceptibility to Manipulation by Sincere Truncation: The Case of Scoring Rules and Scoring Runoff Systems

Self Cite

In a weighted voting game, each voter has a given weight and a coalition of voters is successful if the sum of its weights exceeds a given quota. Such voting systems translate the idea that voters are not all equal by assigning them different weights. In such a situation, two voters are symmetric in a game if interchanging the two voters leaves the outcome of the game unchanged. Two voters with the same weight are naturally symmetric in every weighted voting game, but the converse statement is not necessarily true. We call this latter type of scenario inconsistent weighting. We investigate the conditions that give rise to such a phenomenon within the class of weighted voting games. We also study how the choice of the quota and the total weight can affect the probability of observing inconsistent weighting. Finally, we investigate various applications where inconsistent weighting is observed.

Section: Infinite Total Weightsmentioning

confidence: 99%

Inconsistent weighting in weighted voting games

Béal¹,

Deschamps²,

Diss³

et al. 2022

Self Cite

“…For more details on the Truncation paradox and its occurrence under the scoring rules, we refer toKamwa (2022) andKamwa and Moyouwou (2021).…”

mentioning

confidence: 99%

On two voting systems that combine approval and preferences: fallback voting and preference approval voting

Kamwa¹

2023

Self Cite

Preference Approval Voting (PAV) and Fallback Voting (FV) are two voting rules that combine approval and preferences, first introduced by Brams and Sanver (2009). Under PAV, voters rank the candidates and indicate which ones they approve of; with FV, they rank only those candidates they approve of. In this paper, we further develop the work of Brams and Sanver (2009) by exploring some other normative properties of FV and PAV. We show among other things that FV and PAV satisfy and fail the same criteria; they possess two properties that AV does not: Pareto optimality and the fact of always electing the Absolute Condorcet winner when he exists. To provide a practical comparison, we evaluate the probabilities of satisfying the Condorcet majority criteria for three-candidate elections and a considerably large electorate, examining FV and PAV alongside other voting rules. Our findings indicate that PAV outperforms the Borda rule in this regard. Furthermore, we observe that in terms of agreement, FV and PAV align more closely with scoring rules than with Approval Voting. Our analysis is performed under the impartial anonymous culture assumption.

Scoring rules, ballot truncation, and the truncation paradox

Kamwa

2022

Self Cite

A voting rule that permits some voters to favor a candidate by providing only the initial segment of their sincere rankings is said to be vulnerable to the truncation paradox. In this paper, we consider four models for counting truncated ballots, optimistic, pessimistic (the most common), averaged, and round-down. Under the impartial anonymous culture assumption, the choice of model generally has a real impact on truncation-paradox vulnerability, but there are exceptions. When the election is decided by a one-shot scoring rule, the optimistic model is invulnerable to the truncation paradox, but all other models are vulnerable. We identify new voting rules immune to the truncation paradox, such as the Modified Borda Count. To obtain a more complete picture of the impact of processing model, we assess the likelihood of the truncation paradox in three-candidate elections with large electorates, focusing not only on oneshot scoring rules but also scoring rules with one-by-one or below-average elimination. Our assessment confirms that the processing model for truncated ballots may really matter.