The DH3 "Dark Horse plus 3 rivals" pathology (Executive summary)

  1. Many voting system "pathologies" or "paradoxes" or "bad behaviors" have been noticed over the years. The most damaging ones are those that occur often and which lead to very serious problems such as election of the winner unanimously agreed to be worst.
  2. The DH3 pathology is horribly (near-maximally) common and horribly (maximally in the 4-candidate case) severe: It occurs whenever there are 3 strong contenders and 1 or more unliked "dark horse" candidates. In the 4-candidate case it assures the worst candidate wins.
  3. It devastates both the Borda voting system and all(?) Condorcet systems based on full rank orderings as votes.
  4. This illustrates the extremely severe reaction ("anaphylactic shock") of these systems to "strategic voters."
  5. But range voting reacts only mildly to strategic voters. In the DH3 scenario, Range has no problem and just elects the best winner.

What is DH3? Put briefly: let the 3 main contenders be A,B,C. The A-voters artificially downgrade the main rivals B,C by raising the dark horses "above" them, and the B- and C-supporters act similarly. (Voters who do not act-thus-strategically are ineffectual, having tiny relative effect compared to the vastly-more-powerful strategic voters.) As a result (in vulnerable voting systems) a dark horse wins.

Story illustrating DH3 in action for Borda count voting

More detailed DH3 discussion

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