Tideman alternative method

Last updated May 22, 2024

Tideman's Alternative Method, also called Alternative Smith or Alternative Schwartz, is an electoral system developed by Nicolaus Tideman which selects a single winner using votes that express preferences.

Procedure

Tideman's Alternative Smith with three in the Smith set Tideman-Alternative-Smith.png — Tideman's Alternative Smith with three in the Smith set

The Alternative Smith procedure is as follows:

Eliminate all candidates outside the Smith set.
If there is more than one candidate remaining, eliminate the last-place candidate as in IRV.
Repeat the procedure until there is only one candidate left.

Features

Strategy-resistance

Alternative Smith strongly resists both strategic nomination and strategic voting by political parties or coalitions (although like every system, it can still be manipulated in some situations). The Smith and runoff components of Smith-runoff cover up each 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, burial (ranking a strong rival last, below weak opponents) can often create 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 to a lesser evil (decapitation) strategy: defeating a greater evil requires voters to rank a strong candidate first, rather than express their sincere beliefs.
- However, if such a candidate exists (with majority support), they will usually be a Condorcet winner, and elected in the first round.

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

Spoiler effects

Alternative Smith 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 highest-ranked cycle.

Comparison table

The following table compares Alternative Smith with other single-winner election methods:

Comparison of voting systems
Criterion:	Majority	Majority loser criterion	Mutual majority criterion	Condorcet winner ^{[Tn 1]}	Condorcet loser	Smith ^{[Tn 1]}	ISDA ^{[Tn 1]}	LIIA	IIA ^{[Tn 1]}	Cloneproof	Monotone	Participation	Reversal	Later-no-harm ^{[Tn 1]}	Later-no-help ^{[Tn 1]}	No favorite betrayal ^{[Tn 1]}
Anti-plurality	No	Yes	No	No	No	No	No	No	No	No	Yes	Yes	No	No	No	Yes
Approval	Yes	No	No	No^{[Tn 2]}	No	Yes	Yes	Yes	Yes^{[Tn 3]}	Yes	Yes	Yes	Yes	No	Yes	Yes
Baldwin	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No	No
Black	Yes	Yes	No	Yes	Yes	No	No	No	No	No	Yes	No	Yes	No	No	No
Borda count	No	Yes	No	No	Yes	No	No	No	No	No	Yes	Yes	Yes	No	Yes	No
Bucklin	Yes	Yes	Yes	No	No	No	No	No	No	No	Yes	No	No	No	Yes	No
Coombs	Yes	Yes	Yes	No	Yes	No	No	No	No	No	No	No	No	No	No	Yes
Copeland	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	Yes	No	Yes	No	No	No
Dodgson	Yes	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No	No
Highest median	Yes	Yes^{[Tn 4]}	No^{[Tn 5]}	No^{[Tn 2]}	No	No	No	Yes	Yes^{[Tn 3]}	Yes	Yes	No^{[Tn 6]}	Depends ^{[Tn 7]}	No	Yes	Yes
Instant-runoff voting	Yes	Yes	Yes	No	Yes	No	No	No	No	Yes	No	No	No	Yes	Yes	No
Kemeny–Young	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	No	Yes	No	No	No
Minimax	Yes	No	No	Yes	No	No	No	No	No	No	Yes	No	No	No	No	No
Nanson	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	Yes	No	No	No
Plurality	Yes	No	No	No	No	No	No	No	No	No	Yes	Yes	No	Yes	Yes	No
Random ballot ^{[Tn 8]}	No	No	No	No	No	No	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Ranked pairs	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	No^{[Tn 6]}	Yes	No	No	No
Schulze	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	Yes	No^{[Tn 6]}	Yes	No	No	No
Tideman alternative	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	No	No	No	No	No	No
Table Notes	1 2 3 4 5 6 7 \|Condorcet, Smith and Independence of Smith-dominated alternatives criteria are incompatible with Independence of irrelevant alternatives, Consistency, Participation, Later-no-harm, Later-no-help, and Favorite betrayal ^{[ clarification needed ]} criteria. 1 2 In Approval, Range, and Majority Judgment, if all voters have perfect information about each other's true preferences, any Majority Condorcet or Majority winner can be strategically forced. In particular if every voter knows that "A or B are the two most-likely to win" and differentiates between the two, then the Condorcet winner, if one exists and is in the set {A,B}, will always win. Laslier, J-F (2006), "Strategic approval voting in a large electorate" (PDF), IDEP Working Papers (405), Marseille, France 1 2 Approval voting, range voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute 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. 1 2 3 In 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. ↑ Highest median can pass or fail reversal symmetry depending on the rounding method used to find the median when there are even numbers of voters. ↑ 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.

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References

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

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[condorcet-iia-incompatibility-1] 1 2 3 4 5 6 7 |Condorcet, Smith and Independence of Smith-dominated alternatives criteria are incompatible with Independence of irrelevant alternatives, Consistency, Participation, Later-no-harm, Later-no-help, and Favorite betrayal ^{[ clarification needed ]} criteria.

[approvalnash-2] 1 2 In Approval, Range, and Majority Judgment, if all voters have perfect information about each other's true preferences, any Majority Condorcet or Majority winner can be strategically forced. In particular if every voter knows that "A or B are the two most-likely to win" and differentiates between the two, then the Condorcet winner, if one exists and is in the set {A,B}, will always win. Laslier, J-F (2006), "Strategic approval voting in a large electorate" (PDF), IDEP Working Papers (405), Marseille, France

[IIA_rating_methods-3] 1 2 Approval voting, range voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute 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.

[4] 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.

[mjmmc-5] 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.

[semipc-6] 1 2 3 In 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.

[mjreversal-7] Highest median can pass or fail reversal symmetry depending on the rounding method used to find the median when there are even numbers of voters.

[8] 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.

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