Tideman_alternative_method References

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.

This method is Smith-efficient, making it a kind of Condorcet method. It uses instant-runoff voting for cycle resolution.

Procedure

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 preferential single-winner election methods:

Comparison of voting systems
Criterion:	Majority	Majority loser criterion	Mutual majority criterion	Condorcet winner	Condorcet loser	Smith	ISDA	LIIA	Cloneproof	Monotone	Participation	Reversal	Later-no-harm	Later-no-help	Polynomial time	Resolvability
Schulze	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	No	Yes	No	No	Yes	Yes
Ranked pairs	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	No	No	Yes	Yes
Tideman alternative	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	No	No	No	No	No	Yes	Yes
Kemeny–Young	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	No	Yes	No	No	No	Yes
Copeland	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	No	Yes	No	No	Yes	No
Nanson	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	Yes	No	No	Yes	Yes
Black	Yes	Yes	No	Yes	Yes	No	No	No	No	Yes	No	Yes	No	No	Yes	Yes
Instant-runoff voting	Yes	Yes	Yes	No	Yes	No	No	No	Yes	No	No	No	Yes	Yes	Yes	Yes
Borda count	No	Yes	No	No	Yes	No	No	No	No	Yes	Yes	Yes	No	Yes	Yes	Yes
Baldwin	Yes	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	Yes	Yes
Bucklin	Yes	Yes	Yes	No	No	No	No	No	No	Yes	No	No	No	Yes	Yes	Yes
Plurality	Yes	No	No	No	No	No	No	No	No	Yes	Yes	No	Yes	Yes	Yes	Yes
Coombs	Yes	Yes	Yes	No	Yes	No	No	No	No	No	No	No	No	No	Yes	Yes
Minimax	Yes	No	No	Yes	No	No	No	No	No	Yes	No	No	No	No	Yes	Yes
Anti-plurality	No	Yes	No	No	No	No	No	No	No	Yes	Yes	No	No	No	Yes	Yes
Dodgson	Yes	No	No	Yes	No	No	No	No	No	No	No	No	No	No	No	Yes

References

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