Tideman alternative method

The Tideman Alternative method, also called[by whom?] Alternative-Smith voting, is a voting rule developed by Nicolaus Tideman which selects a single winner using ranked ballots. This method is Smith-efficient, making it a Condorcet method, and uses instant-runoff voting to resolve any cyclic ties.

Procedure

Tideman's Alternative Smith with three in the Smith set

Tideman's rule starts with all candidates and proceeds to eliminate candidates as follows, halting when only one candidate remains:

  1. From the remaining candidates, eliminate all who are not in the top cycle (most often defined as the Smith set). Go to Step 2.
  2. From the remaining candidates, eliminate the candidate ranked first by the fewest voters. Go to Step 1.

When a candidate is eliminated, their name is stricken from all ballots and the remaining candidates are renumbered first, second, third, etc. The procedure can also be applied using 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 can still be manipulated in some situations). The Smith and runoff components of the system each cover the other's weaknesses:

  1. 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 be used to manufacture a false cycle.
  2. 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 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 highest-ranked cycle.

Comparison table

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

This table is incomplete; you can help by adding missing items.
Comparison of single-winner voting systems
Criterion


Method
Majority winner
 Ballot type
Plurality Yes No No No No Yes 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 No No Yes Yes Yes No Yes No No Yes Single mark
Two round system Yes Yes No No Yes Yes No No No No No No No Yes Yes Yes No Single mark
Instant-runoff Yes Yes Yes No Yes 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 No Yes No No Yes Ranking
Nanson Yes Yes Yes Yes Yes Yes No 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 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 No Yes No No No Yes No Yes No No No Yes No No No Ranking
Copeland Yes Yes Yes Yes Yes Yes Yes Yes No No No Yes No No No No No Ranking
Black Yes Yes No Yes Yes Yes No No No No No Yes No No Yes Yes No No No Ranking
Kemeny Yes Yes Yes Yes Yes Yes Yes Yes LIIA No No Yes No No Yes Yes No No No Ranking
Ranked pairs Yes Yes Yes Yes Yes Yes Yes Yes LIIA No Yes Yes No No Yes Yes No No No Ranking
Schulze Yes Yes Yes Yes Yes Yes Yes Yes No No Yes Yes No No Yes Yes No No No Ranking
Borda No Yes No No Yes Yes No No No No No Yes Yes Yes Yes Yes No Yes No Ranking
Bucklin Yes Yes Yes No No No No No No No Yes No No No Yes No Yes No Ranking
Dodgson Yes No No Yes No No No No No No No No No No No No No Ranking
Approval Yes No No No No Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Approvals
Majority Judgement No No No No No No Yes Yes Yes Yes No No Yes No Yes Yes Scores
Score No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Scores
STAR No Yes No No Yes No No No No No Yes No No No No No No Scores
Quadratic No No No No No No No No No Yes Yes Yes N/A N/A No Credits
Random ballot No No No No No Yes No Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Single mark
Maximal lotteries Yes Yes Yes Yes Yes Yes Yes No Yes No Yes No No Ranking
Sortition No No No No No No No Yes Yes No No Yes N/A Yes N/A N/A Yes Yes Yes None
Table Notes
  1. 1 2 3 4 5 6 7 Condorcet's criterion is incompatible with the consistency, independence of irrelevant alternatives, participation, later-no-harm, later-no-help, and sincere favorite criteria.
  2. 1 2 A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.
  3. 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.
  4. 1 2 3 Approval voting, score 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.
  5. ↑ 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.
  6. ↑ 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.
  7. ↑ A randomly chosen ballot determines the winner. It is the unique social choice rule that treats all voters equally while still being strategyproof in all situations.
  8. ↑ Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.

References