Runoff: Difference between revisions
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{{Distinguish|Runoff voting}}
<small>[This article combines three separate concepts: runoffs, elections with only two major candidates in them, and binary votes].</small>
A runoff (or binary vote, or [[pairwise]] comparison) is when two candidates face off in a separate (usually second) round of an election, with the winner of the runoff being the winner of the overall election. Usually [[choose-one FPTP voting]] is used for the runoff, though any voting method could be considered ([[Score voting]] being one of the more interesting to consider). More abstractly, it is when voters choose between two options. ▼
▲A runoff (or binary vote, or [[pairwise]] comparison) is when two candidates face off in a
Voting honestly in an FPTP-based (or FPTP-equivslent runoff, if using something like [[STAR]] in the runoff on the assumption voters indicate all of their preferences) can never hurt a voter, because either the voter's preferred candidate wins with the added support of that voter where they otherwise wouldn't have, or they end up losing either way, with the voter's vote only reducing the margin of defeat between the two candidates in the runoff.▼
▲Voting honestly in an FPTP-based (or FPTP-
If FPTP is used in the runoff, then either one candidate is guaranteed to have a majority of votes, or both candidates are tied.
Binary votes are fundamental to voting theory, because they have a number of desirable properties (strategyproofness, or if using [[utilitarian voting]], no incentive for coordinated strategic voting i.e. strategic voting is simple and simply involves exaggerating your preference such that you max score your preferred option and min score the other option) that are impossible when there are more than two candidates/options to vote on. See the [[Gibbard-Satterthwaite theorem]] for more information. ▼
=== Automatic runoff ===
The normal version of a runoff (with a separate election) is often called a "delayed" runoff. [[RCV]] (also sometimes called instant-runoff voting) and [[STAR voting]] both can be thought of as involving an automatic or instant runoff (meaning the runoff is done using the same ballots as were used to find the result of one of the previous rounds) which determines the winner.
Runoffs can be defined as a [[Pairwise
== Criticisms ==
Adding a runoff to a voting method often breaks several desirable properties of the underlying voting method, and adds potential for certain nonintuitive [[Strategic voting|voting strategies]] such as [[pushover]]. For example, [[Score voting]] passes several generalized forms of [[Monotonicity]] and [[Favorite Betrayal]], but neither its instant-runoff version, [[STAR voting]], nor the delayed/separate-runoff version have those properties. Example:<blockquote>9: A:5 B:1 C:0▼
=== Political faction violence ===
Delayed runoffs may actually encourage violence on the part of factions whose preferred candidates didn't make it into the runoff, because there is a period of time in which they are aware they will not get what they want.
=== Lack of voter choice ===
An abstract criticism of two-candidate elections in general is that they reduce voter choice; indeed, one major reason voting reform advocates wish to move away from [[FPTP]] for single-winner races is to encourage more candidates to run, and more popular candidates to win.
Runoffs are also subject to this criticism, albeit to a lesser degree, because voters can't support candidates who are not in the runoff.
==== Write-in option ====
The use of a [[write-in option]] in the runoff, combined with a voting method that allows for supporting multiple candidates (i.e. [[rated method]] or [[Condorcet methods]]), would allow alternative candidates to pick up support in the runoff. However, this breaks the strategyproofness of runoffs (see below).
=== Majoritarianism ===
By only offering two choices, it is often postulated that runoffs encourage candidates to campaign in a divisive manner to simply ensure more than half of the voters prefer them to their opponent, which may arbitrarily divide the electorate into two rival factions.
=== Strategic voting ===
While a runoff itself is strategyproof, the elections/rounds before the runoff are not. Because they are a type of [[Multiple-round voting method]], runoffs are susceptible to some unusual forms of strategic voting, such as [[pushover]]; adding a runoff to a voting method often breaks several desirable properties of the underlying voting method.
==== Example for STAR voting ====
▲
12 B:5 C:1 A:0
Line 19 ⟶ 44:
8 C:5 A:1 B:0</blockquote>The score totals are A 53, B 69, C 52. A and B go to the automatic runoff, and then A [[Pairwise beat|pairwise beats]] B 17 to 12 and wins. But if the 12 B:5 C:1 A:0 voters had instead voted B:5 C:4 A:0, they would've helped C enter the automatic runoff instead of A, where B pairwise beats C and wins instead. This is nonintuitive because by increasing their support for an [[Independence of irrelevant alternatives|irrelevant alternative]], the B-top voters made their favorite win. <ref>{{Cite web|url=https://rangevoting.org/StarVoting.html|title="STAR voting"|last=|first=|date=|website=|url-status=live|archive-url=|archive-date=|access-date=}}</ref> This is essentially because this is a [[Condorcet cycle]] situation, so any voting method passing the [[Majority criterion|majority criterion]] in the two-candidate case, such as any voting method ending with a runoff, will shift its results depending on, when there are only two candidates in the election, who the two are.
== Binary vote ==
▲See [[:Category:Runoff-based voting methods|Category:Runoff-based voting methods]].
=== Two-candidate case ===
A runoff can be thought of as the electoral (candidate-based) instance of a binary vote, which is simply any time voters choose between two options. For example, [[legislative voting]] often involves choosing between passing a bill or not passing it (i.e. staying with the status quo).
=== Strategyproofness ===
▲Binary votes are fundamental to voting theory, because they have a number of desirable properties (strategyproofness, or if using [[utilitarian voting]], no incentive for coordinated strategic voting i.e. the only [[strategic voting]]
== See also ==
* [[Pairwise preference]]
* [[Utility#Two-candidate case]]
* [[Condorcet method]]
[[Category:Majority-related concepts]]
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