Ranked voting in the context of "Supplementary vote"

Indirect single transferable voting or Gove system is a version of single transferable vote (STV), where the vote transfer is determined by the candidate's instructions, not voter's marked preferences. This system produces many of the benefits of STV without the complexity of a ranked voting system. Under indirect STV, there would be no need to concentrate the votes in one place for vote transfers to be performed.

Indirect STV was invented by Walter Baily, of Leeds, and put forward in his 1872 book PR in Large Constituencies.Massachusetts legislator William H. Gove of Salem and Archibald E. Dobbs of Ireland, author of Representative Reform for Ireland (1879), both were early and strong supporters.

Ranked-choice voting (RCV) can refer to one of several ranked voting methods used in some cities and states in the United States. The term is not strictly defined, but most often refers to instant-runoff voting (IRV) or single transferable vote (STV), the main difference being whether only one winner or multiple winners are elected. At the federal and state level, instant-runoff voting is used for congressional and presidential elections in Maine; state, congressional, and presidential general elections in Alaska; and special congressional elections in Hawaii. Since 2025, it is also used for all elections in the District of Columbia.

Single transferable voting, only possible in multi-winner contests, is not currently used in state or congressional elections. It is used to elect city councillors in Portland, Oregon, Cambridge, Mass., and several other cities.

Instant-runoff voting (IRV; US: ranked-choice voting (RCV), AU: preferential voting, UK/NZ: alternative vote) is a single-winner ranked voting election system where one or more eliminations are used to simulate multiple runoff elections. In each round, the candidate with the fewest first-preference votes (among the remaining candidates) is eliminated. This continues until only one candidate is left. Instant runoff falls under the plurality-with-elimination family of voting methods, and is thus closely related to methods like the two-round runoff system and party primary systems.

Instant-runoff voting has found some use in national elections in several countries, predominantly in the Anglosphere. It is used to elect members of the Australian House of Representatives and the National Parliament of Papua New Guinea, and to elect the head of state in India, Ireland, and Sri Lanka.

In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold:

1. The process is dictatorial, i.e. there is a single voter whose vote chooses the outcome.
2. The process limits the possible outcomes to two options only.
3. The process is not straightforward; the optimal ballot for a voter "requires strategic voting", i.e. it depends on their beliefs about other voters' ballots.

A corollary of this theorem is the Gibbard–Satterthwaite theorem about voting rules. The key difference between the two theorems is that Gibbard–Satterthwaite applies only to ranked voting. Because of its broader scope, Gibbard's theorem makes no claim about whether voters need to reverse their ranking of candidates, only that their optimal ballots depend on the other voters' ballots.

In electoral systems which use ranked voting, a donkey vote (also known as an alphabet vote) is a cast ballot where the voter ranks the candidates based on the order they appear on the ballot itself. The voter that votes in this manner is referred to as a donkey voter.

Typically, this involves numbering the candidates in the order they appear on the ballot paper: first preference for the first-listed candidate, second preference for the second-listed candidate, and so on. However, donkey votes can also occur in reverse, such that someone numbers the candidates from the bottom up the ballot paper. In systems where a voter is required to place a number against each candidate for the vote to be valid, the voter may give the first preference to the candidate they prefer, then run all the other numbers donkey fashion.

Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, Arrow showed no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrelated option, C.

The result is often cited in discussions of voting rules, where it shows no ranked voting rule can eliminate the spoiler effect. This result was first shown by the Marquis de Condorcet, whose voting paradox showed the impossibility of logically-consistent majority rule; Arrow's theorem generalizes Condorcet's findings to include non-majoritarian rules like collective leadership or consensus decision-making.