Ranked voting
Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties.
Copeland's method was devised by Ramon Llull in his 1299 treatise Ars Electionis, which was discussed by Nicholas of Cusa in the fifteenth century.
This methodology drew criticism from the Marquis de Condorcet, who developed his own methods after arguing Borda's approach did not accurately reflect group preferences, because it was vulnerable to spoiler effects and did not always elect the majority-preferred candidate.
Danish pioneer Carl Andræ formulated the single transferable vote system, which was adopted by his native Denmark in 1855.
[8] Theoretical exploration of electoral processes was revived by a 1948 paper from Duncan Black[9] and Kenneth Arrow's investigations into social choice theory, a branch of welfare economics that extends rational choice to include community decision-making processes.
[citation needed] A form of the single transferable vote system was invented by Carl Andræ in Denmark, where it was used briefly before being abandoned for direct elections in favor of the simpler open list rules.
[12] The single transferable vote system has also been used to elect legislators in Canada, South Africa and India.
[15][16] After a series of electoral pathologies in Alaska's 2022 congressional special election, a poll found 54% of Alaskans supported a repeal of the system.
In instant runoff and first-preference plurality, such ballots are generally rejected; however, in social choice theory some election systems assume equal-ranked ballots are "split" evenly between all equal-ranked candidates (e.g. in a two-way tie, each candidate receives half a vote).
Meanwhile, other election systems, the Borda count and the Condorcet method, can use different rules for handling equal-rank ballots.
Many concepts formulated by the Marquis de Condorcet in the 18th century continue to significantly impact the field.
[23] Spatial voting models, initially proposed by Duncan Black and further developed by Anthony Downs, provide a theoretical framework for understanding electoral behavior.
It is assumed that voters tend to favor candidates who closely align with their ideological position over those more distant.
The accompanying diagram presents a simple one-dimensional spatial model, illustrating the voting methods discussed in subsequent sections of this article.
Spatial models offer significant insights because they provide an intuitive visualization of voter preferences.
Gibbard's theorem provides a closely-related corollary, that no voting rule can have a single, always-best strategy that does not depend on other voters' ballots.
The Borda count is a weighted-rank system that assigns scores to each candidate based on their position in each ballot.
It elects any candidates who achieve quota, and if necessary recursively eliminates the plurality loser at each stage of the vote count and transfers surplus votes of winners until enough are elected by quota or by still being in the running when the field of candidates is thinned to the number of remaining open seats.
