Tideman alternative method


The Tideman Alternative method, also called 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 the alternative vote to resolve any cyclic ties.

Procedure

The procedure for Tideman's rule is as follows:
  1. Eliminate all candidates who are not in the top cycle.
  2. If there is more than one candidate remaining, eliminate the candidate ranked first by the fewest voters.
  3. Repeat the procedure until there is a Condorcet winner, at which point the Condorcet winner is elected.
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. 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.
  2. * This reasoning does not apply to situations with a Condorcet cycle, however.
  3. * While Condorcet cycles are rare in practice with honest voters, burial can often be used to manufacture a false cycle.
  4. 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.
  5. * 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".
  6. * 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. This method states that if one candidate wins an election, and a new alternative 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: