arXiv subjects

Jennifer Wilson

Publications and source records attributed to Jennifer Wilson.

7 recordsLinked to original sources

arXiv2026

Can ranked-choice voting elect the least popular candidate?

We analyze how frequently instant runoff voting (IRV) selects the weakest (or least popular) candidate in three-candidate elections. We consider four definitions of ``weakest candidate'': the Borda loser, the Bucklin loser, the candidate with the most last-place votes, and the candidate with minimum social utility. We determine the probability that IRV selects the weakest candidate under the impartial anonymous culture and impartial culture models of voter behavior, and use Monte Carlo simulations to estimate these probabilities under several spatial models. We also examine this question empirically using a large dataset of real elections. Our results show that IRV can select the weakest candidates under each of these definitions, but such outcomes are generally rare. Across most models, the probability that IRV elects a given type of weakest candidate is at most 5\%. Larger probabilities arise only when the electorate is extremely polarized.

econ.GN↗

arXiv2026

Bloc Voting on Single Peaked Preferences

We analyze the winning coalitions that arise under Bloc voting when voters preferences are single-peaked. For small numbers of candidates and numbers of winners, we determine conditions under which candidates in winning coalitions are adjacent. We also analyze the results of pairwise contests between winning and losing candidates and assess when the winning coalitions satisfy several proposed extensions of the Condorcet criterion to multiwinner voting methods. Finally, we use Monte Carlo simulations to investigate how frequently these coalitions arise under different assumptions about voter behavior.

cs.GT↗

arXiv2025

Sequential Apportionment from Stationary Divisor Methods

Divisor methods are well known to satisfy house monotonicity, which allows representative seats to be allocated sequentially. We focus on stationary divisor methods defined by a rounding cutpoint $c \in [0,1]$. For such methods with integer-valued votes, the resulting apportionment sequences are periodic. Restricting attention to two-party allocations, we characterize the set of possible sequences and establish a connection between the lexicographical ordering of these sequences and the parameter $c$. We then show how sequences for all pairs of parties can be systematically extended to the $n$-party setting. Further, we determine the number of distinct sequences in the $n$-party problem for all $c$. Our approach offers a refined perspective on size bias: rather than viewing large parties as simply receiving more seats, we show that they instead obtain their seats earlier in the apportionment sequence. Of particular interest is a new relationship we uncover between the sequences generated by the smallest divisor (Adams) and greatest divisor (D'Hondt or Jefferson) methods.

math.GM↗

arXiv2025

Instant Runoff Voting and the Reinforcement Paradox

We analyze the susceptibility of instant runoff voting (IRV) to a lesser-studied paradox known as a \emph{reinforcement paradox}, which occurs when candidate $X$ wins under IRV in two distinct elections but $X$ loses in the combined election formed by merging the ballots from the two elections. For three-candidate IRV elections we provide necessary and sufficient conditions under which there exists a partition of the ballot set into two sets of ballots such that a given losing candidate wins each of the sub-elections. Applying these conditions, we use Monte Carlo simulations to estimate the frequency with which such partitions exist under various models of voter behavior. We also analyze the frequency with which the paradox occurs in a large dataset of real-world ranked-choice elections to provide empirical probabilities. Our general finding is that IRV is highly susceptible to this paradox in three-candidate elections.

physics.soc-ph↗

arXiv2024

The Negative Participation Paradox in Three-Candidate Instant Runoff Elections

In this paper, we provide theoretical and empirical estimates for the likelihood of a negative participation paradox under instant runoff voting in three-candidate elections. We determine the probability of the paradox and related conditional probabilities based on the impartial anonymous culture and impartial culture models for both complete and partial ballots. We compare these results to the empirical likelihood of a negative participation paradox occurring under instant runoff voting in a large database of voter profiles which have been reduced to three candidates. Lastly, we analyze the relative likelihood of this paradox in comparison to other well-known paradoxes.

physics.soc-ph↗

arXiv2024

Multiwinner Elections and the Spoiler Effect

In the popular debate over the use of ranked-choice voting, it is often claimed that the method of single transferable vote (STV) is immune or mostly immune to the so-called ``spoiler effect,'' where the removal of a losing candidate changes the set of winners. This claim has previously been studied only in the single-winner case. We investigate how susceptible STV is to the spoiler effect in multiwinner elections, where the output of the voting method is a committee of size at least two. To evaluate STV we compare it to numerous other voting methods including single non-transferable vote, $k$-Borda, and the Chamberlin-Courant rule. We provide simulation results under three different random models and empirical results using a large database of real-world multiwinner political elections from Scotland. Our results show that STV is not spoiler-proof in any meaningful sense in the multiwinner context, but it tends to perform well relative to other methods, especially when using real-world ballot data.

stat.ME↗

arXiv2000

Clustering of Very Red Galaxies in the Las Campanas IR Survey

We report results from the first 1000 square arc-minutes of the Las Campanas IR survey. We have imaged 1 square degree of high latitude sky in six distinct fields to a 5-sigma H-band depth of 20.5 (Vega). Optical imaging in the V,R,I,and z' bands allow us to select color subsets and photometric-redshift-defined shells. We show that the angular clustering of faint red galaxies (18 < H < 20.5, I - H > 3) is an order of magnitude stronger than that of the complete H-selected field sample. We employ three approaches to estimate $n(z)$ in order to invert w(theta) to derive r_0. We find that our n(z) is well described by a Gaussian with = 1.2, sigma(z) = 0.15. From this we derive a value for r_0 of 7 (+2,-1) co-moving H^{-1} Mpc at = 1.2. This is a factor of ~ 2 larger than the clustering length for Lyman break galaxies and is similar to the expectation for early type galaxies at this epoch.

astro-ph↗