View source for Tideman alternative method

{{Short description|Single-winner electoral system family}}
{{Electoral systems sidebar|expanded=Single-winner}}The '''Tideman Alternative method''', also called{{by who?|date=October 2024}} [[Alternative vote|'''Alternative''']]-[[Smith set|'''Smith''']] '''voting''', is a [[Electoral systems|voting rule]] developed by [[Nicolaus Tideman]] which selects a single winner using [[Ranked voting|ranked ballots]]. This method is [[Smith criterion|Smith]]-efficient, making it a kind of [[Condorcet method]], and uses the [[Instant-runoff voting|alternative vote]] ([[Instant-runoff voting|RCV]]) to resolve any [[Condorcet paradox|cyclic ties]].

== Procedure ==
[[File:Tideman-Alternative-Smith.png|right|thumb|Tideman's Alternative Smith with three in the Smith set]]
The procedure for Tideman's rule is as follows:

# Eliminate all candidates who are not in the [[top cycle]] (most often defined as the [[Smith set]]).
# If there is more than one candidate remaining, [[Instant runoff voting|eliminate the candidate ranked first by the fewest voters]].
# Repeat the procedure until there is a [[Condorcet winner criterion|Condorcet winner]], at which point the Condorcet winner is elected.

The procedure can also be applied using [[Tournament set|tournament sets]] other than the Smith set, e.g. the [[Landau set]], [[Copeland set]], or [[bipartisan set]].

== Features ==
=== Strategy-resistance ===
Tideman's Alternative strongly resists both [[strategic nomination]] and [[strategic voting]] by political parties or coalitions (although like every system, it [[Gibbard–Satterthwaite theorem|can still be manipulated]] in some situations). The Smith and [[Instant-runoff voting|runoff]] components of the system each cover the other's weaknesses:

# Smith-efficient methods are difficult for any coalition to manipulate, because no majority-strength coalition will have an incentive to remove a Condorcet winner: if most voters prefer A to B,  A can ''already'' defeat B.
#* This reasoning does not apply to situations with a [[Condorcet cycle]], however.
#* While Condorcet cycles are rare in practice with honest voters, [[Strategic voting|burial]] (ranking a strong rival last, below weak opponents) can often be used to manufacture a false cycle.
# [[Instant run-off voting|Instant runoff voting]] is resistant to burial, because it is only based on each voter's top preference in any given round. This means that burial strategies effective against the Smith-elimination step are not effective against the instant runoff step.
#* On the other hand, instant-runoff voting is highly vulnerable to [[Strategic voting#Compromising|compromising]] strategy, where voters are incentivized to rank "lesser evils" higher in order to defeat a "greater evil".
#* However, if a Condorcet winner exists, they're immune to compromising, so electing them reduces compromise incentive.

The combination of these two methods creates a highly strategy-resistant system.

=== Spoiler effects ===
Tideman's Alternative fails [[independence of irrelevant alternatives]], meaning it can sometimes be affected by spoiler candidates. However, the method adheres to a weaker property that eliminates most spoilers, sometimes called [[independence of Smith-dominated alternatives]] (ISDA). This method states that if one candidate (X) wins an election, and a new alternative (Y) is added, X will still win the election as long as Y is not in the [[Smith set|highest-ranked cycle]].

=== Comparison table ===
The following table compares Tideman's Alternative with other single-winner election methods:{{Comparison of Schulze to preferential voting systems}}

== References ==
<references group="vs" />
* Green-Armytage, James. [http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf Four Condorcet-Hare Hybrid Methods for Single-Winner Elections].

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[[Category:Single-winner electoral systems]]