Strategic voting in the context of "Gibbard's theorem"

Voting is the process of choosing one or more officials or representatives by casting an oral vote or a ballot, a document that formally expresses voter's preference or preferences as to whom should be elected or whom the voter likes and thinks has best chance to be elected. Voting can also be used to decide on policy usually by a majority but sometimes a super-majority is required. In Republics and representative democracies, a portion of the population votes to choose representative government members.

Electoral systems, the procedure for converting votes cast into winners, vary depending on both the country and the political office. In many countries organizations work to reform the election system, usually to make it fairer and ensure that as many votes as possible are used to elect the winners.

Cumulative voting (sometimes called the single divisible vote) is an election system where a voter casts multiple votes but can lump votes on a specific candidate or can split their votes across multiple candidates. The candidates elected are those receiving the largest number of votes cast in the election, up to the number of representatives to be elected.

Cumulative voting can simplify strategic voting, by allowing larger groups of voters to elect multiple representatives by splitting their vote between multiple candidates. This removes the complexity associated with randomized or coordinated strategies.

In political science and social choice, Black's median voter theorem says that if voters and candidates are distributed along a political spectrum, any Condorcet consistent voting method will elect the candidate preferred by the median voter. The median voter theorem thus shows that under a realistic model of voter behavior, Arrow's theorem does not apply, and rational choice is possible for societies. The theorem was first derived by Duncan Black in 1948, and independently by Kenneth Arrow.

Similar median voter theorems exist for rules like score voting and approval voting when voters are either strategic and informed or if voters' ratings of candidates fall linearly with ideological distance.