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Tideman alternative method

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TheTideman Alternative method, also called^{[by whom?]}Alternative-Smithvoting, is avoting rule developed byNicolaus Tideman which selects a single winner usingranked ballots. This method isSmith-efficient, making it aCondorcet method, and uses thealternative vote (RCV) to resolve anycyclic ties.

Procedure

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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 thetop cycle (most often defined as theSmith set).
If there is more than one candidate remaining,eliminate the candidate ranked first by the fewest voters.
Repeat the procedure until there is aCondorcet winner, at which point the Condorcet winner is elected.

The procedure can also be applied usingtournament sets other than the Smith set, e.g. theLandau set,Copeland set, orbipartisan set.

Features

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Strategy-resistance

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Tideman's Alternative strongly resists bothstrategic nomination andstrategic voting by political parties or coalitions (although like every system, itcan still be manipulated in some situations). The Smith andrunoff 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 canalready defeat B.
- This reasoning does not apply to situations with aCondorcet cycle, however.
- While Condorcet cycles are rare in practice with honest voters,burial (ranking a strong rival last, below weak opponents) can often be used to manufacture a false cycle.
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 tocompromising 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

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Tideman's Alternative failsindependence 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 calledindependence 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 thehighest-ranked cycle.

Comparison table

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The following table compares Tideman's Alternative with other single-winner election methods:

Comparison of single-winner voting systems
Criterion Method	Majority winner	Majority loser	Mutual majority	Condorcet winner^{[Tn 1]}	Condorcet loser	Smith^{[Tn 1]}	Smith-IIA^{[Tn 1]}	IIA/LIIA^{[Tn 1]}	Cloneproof	Monotone	Consistency	Participation	Reversal symmetry	Homogeneity	Later-no-harm^{[Tn 1]}	Later-no-help^{[Tn 1]}	No favorite betrayal^{[Tn 1]}	Ballot type
First-past-the-post	Yes	No	No	No	No	No	No	No	No	Yes	Yes	Yes	No	Yes	Yes	Yes	No	Single mark
Anti-plurality	No	Yes	No	No	No	No	No	No	No	Yes	Yes	Yes	No	Yes	No	No	Yes	Single mark
Two round system	Yes	Yes	No	No	Yes	No	No	No	No	No	No	No		Yes	Yes	Yes	No	Single mark
Instant-runoff	Yes	Yes	Yes	No	Yes	No	No	No	Yes	No	No	No	No	Yes	Yes	Yes	No	Ranking
Coombs	Yes	Yes	Yes	No	Yes	No	No	No	No	No	No	No		Yes	No	No	Yes	Ranking
Nanson	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	Yes		No	No	No	Ranking
Baldwin	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No		No	No	No	Ranking
Tideman alternative	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	No	No	No	No		No	No	No	Ranking
Minimax	Yes	No	No	Yes^{[Tn 2]}	No	No	No	No	No	Yes	No	No	No		No^{[Tn 2]}	No	No	Ranking
Copeland	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	No	No			No	No	No	Ranking
Black	Yes	Yes	No	Yes	Yes	No	No	No	No	Yes	No	No	Yes	Yes	No	No	No	Ranking
Kemeny	Yes	Yes	Yes	Yes	Yes	Yes	Yes	LIIA Only	No	Yes	No	No	Yes	Yes	No	No	No	Ranking
Ranked pairs	Yes	Yes	Yes	Yes	Yes	Yes	Yes	LIIA Only	Yes	Yes	No	No^{[Tn 3]}	Yes	Yes	No	No	No	Ranking
Schulze	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	No	No^{[Tn 3]}	Yes	Yes	No	No	No	Ranking
Borda	No	Yes	No	No	Yes	No	No	No	No	Yes	Yes	Yes	Yes	Yes	No	Yes	No	Ranking
Bucklin	Yes	Yes	Yes	No	No	No	No	No	No	Yes	No	No	No	Yes	No	Yes	No	Ranking
Approval	Yes	No	No	No	No	No	No	Yes^{[Tn 4]}	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	Approvals
Majority Judgement	No	No^{[Tn 5]}	No^{[Tn 6]}	No	No	No	No	Yes^{[Tn 4]}	Yes	Yes	No	No^{[Tn 3]}		Yes	No	Yes	Yes	Scores
Score	No	No	No	No	No	No	No	Yes^{[Tn 4]}	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	Scores
STAR	No	Yes	No	No	Yes	No	No	No	No	Yes	No	No	No		No	No	No	Scores
Quadratic	No	No	No	No	No	No	No	No	No	Yes		Yes			N/A	N/A	No	Credits
Random ballot^{[Tn 7]}	No	No	No	No	No	No	No	Yes	Yes	Yes		Yes		Yes	Yes	Yes	Yes	Single mark
Sortition^{[Tn 8]}	No	No	No	No	No	No	No	Yes	No	Yes		Yes		N/A	Yes	Yes	Yes	None
Table Notes	^^a ^b ^c ^d ^e ^f ^gCondorcet's criterion is incompatible with theconsistency,independence of irrelevant alternatives,participation,later-no-harm,later-no-help, andsincere favorite criteria. ^^a ^bA variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm. ^^a ^b ^cIn Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one. ^^a ^b ^cApproval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their ownabsolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates. ^Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters. ^Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade. ^A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria. ^Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.

References

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Green-Armytage, James.Four Condorcet-Hare Hybrid Methods for Single-Winner Elections.

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