Index of Interesting Examples of Election Pathologies on the CRV website

• "Add top" failure in BTR-IRV & Rouse voting methods; adding votes ranking X top causes X to lose, this is one example of a general theorem that in every Condorcet voting method, add-top or add-bottom (or both) failure election-scenarios exist. (But range voting never exhibits add-top or add-bottom failure.)
• Simplest example of a conflict between Approval and Condorcet winners, used as preface to general theorem that no such conflict exists under certain assumptions about voter behavior;
• Simple example of situation where honest range voters elect somebody who is not the (traditionally defined) Condorcet winner (but range always elects a Condorcet winner according to a nontraditional definition); an argument that the nontraditional definition is a better idea is the "free the slaves" example;
• Fishburn example of a pure-rank-order-ballot election where (a) a unique Condorcet winner exists, (b) most people would agree it is the "wrong" winner. Condorcet self-contradiction example. Related example where every weighted-positional voting system agrees that B wins but every Condorcet voting system says A wins.
• Poison pills are a common parliamentary trick that depend on the creation and exploitation of Condorcet cycles.
• Favorite Betrayal works to elect the "lesser evil"; this is a general purpose example that works for almost every ranked-ballot method ever seriously proposed including all Condorcet methods (and this is what you get after the betrayal); illustrates "spoiler" effect which is what leads to 2-party domination; (But range voting never exhibits favorite betrayal); also in this example, if C is deleted, then A wins instead of B, illustrating the fact that ex post facto deletion of "irrelevant losers" can alter election results in almost every ranked-ballot system ever seriously proposed (but that never happens in range voting);
• IRV example where voting maximally for somebody makes him lose but voting maximally against him makes him win; (can never happen with range voting) Another such IRV example.
• IRV example where IRV refuses to elect Condorcet winner (and demonstrates "IRV spoiler pathology")
• IRV example where IRV refuses to elect Condorcet winner even though has more top-rank votes than the IRV winner
• "Top-3-only" bastardized IRV – plenty of things can go wrong with that that go beyond the things that can go wrong with ordinary IRV.
• IRV non-monotonicity.
• Simple IRV spoiler example.
• IRV non-additivity example (why IRV cannot be counted in precincts).
• Condorcet non-additivity example (somewhat analogous)
• IRV "amplification" phenomenon that can lead to "chaos"; related Unger examples where IRV elects somebody who would lose pairwise by large margins to every opponent but one (whom beats by only 1 vote), and this IRV winner is the same candidate as the IRV "worst" candidate, i.e. who would win using IRV on all-reversed-votes.
• Voting honestly in IRV can be worse for you than not voting at all (but in range voting, that can never happen); also illustrates "favorite betrayal" and "spoiler" and "lesser evil" pathologies in IRV;
• Another structure of IRV favorite-betrayal examples
• IRV winner=loser pathology (reversal failure; winner=loser can never happen with range voting, Borda, Schulze beatpaths, Tideman ranked pairs, Approval unless all tied); also illustrates a no-show paradox (honest votes hurt you) and bizarre lying techniques (maximally dishonest total-lie vote is better for you than an honest one); (with range voting, honest votes never can hurt you versus not voting at all)
• Simple explanations of how the Peru 2006 pathology could have happened under IRV (also same thing happened in Chile 1970);
• The French study gives an example from real life where the approval-voting election winner had below 50% approval.
• 6 different winners in 6 different voting systems;
• In many voting systems best strategy for a cofeeling voter subset is not for them all to vote in the same way (but with range voting, all-vote-same is best strategy for a co-feeling group);
• All of the simplest nonmonotonic IRV elections (in contrast, range voting is monotonic);
• Nontransitive dice
• Borda "cloning helps" example (in contrast, cloning never helps or hurts in range voting);
• Borda example by Johnson where ex post facto deletion of an "irrelevant loser" leads to complete reversal of all other election results (in contrast, this kind of deletion of somebody never affects the range voting winner or results order unless the deletee was the winner);
• Simple example of range vs IRV (done both ways) election where, under IRV, voting honestly for X makes X lose
• IRV elects D but an approximately 2:1 supermajority prefers C over both D and everybody else too; also Dave Ketchum gives a similar example;
• Same theme taken to an extreme: In Puzzle 18, IRV refuses to elect a candidate preferred by 99:1 or larger supermajorities over every other candidate (and ranked top or second-top by every voter);
• IRV example by Brams showing numerous pathologies including how "truncating" your vote can be better than an honest IRV vote, and how raising your vote for B from bottom to top can cause B to lose;
• Several examples involving randomness or incomplete information in which best range voting strategy is not "Approval style" (although under certain approximate assumptions, an approval-style range vote, or something extremely close to it, always is strategically best)
• Several 4-candidate examples involving randomness or incomplete information in which best range voting strategy is dishonest (but with ≤3 candidates best range vote always is at least "semi-honest" and refuses to reverse an A>B relation among two candidates);
• Thomas Smith illustrates a classic debate between Borda & Condorcet and shows how range voting resolves the debate using intensity information unavailable to Borda and Condorcet;
• Adam Tarr's realistic example where favorite betrayal (to elect the "lesser evil") is best voter strategy in IRV (causing "spoiler" effect, leading to 2-party domination);
• Kevin Venzke proves that winning votes Condorcet with "candidate-equalities permitted in votes" still exhibits "favorite betrayal" (aka. "spoiler effect," "lesser-evil") of the sort that engenders Duverger law 2-party domination (but favorite betrayal never happens with range voting); simpler example by Warren Smith of the same thing;
• Venzke's brilliantly simple proof that "favorite betrayal" is sometimes "strategically forced" in every Condorcet voting method (whether rank-equalities are allowed or not).
• The DH3 pathology (also described in more detail here and especially here) which is an enormously severe and common pathology afflicting Borda and Condorcet voting systems and caused by strategic voting (but plurality, IRV, range, and approval are immune to it);
• Example by Juho Laatu where "winning votes" Condorcet looks pretty stupid compared to "margins";
• But "winning votes" Condorcet looks good versus "margins" in this example where it avoids "favorite betrayal" but margins does not;
• Portugal 1986 probable real world example of J.H.Nagel's "Burr dilemma" pathology of approval voting showing that for strategic reasons "vote splitting" still is possible with Approval (but range voting should diminish this effect);
• World's largest dataset of real world presidential-level "wrong way elections";
• Puzzle 31 shows how removing a single candidate can cause the election results (in any weighted positional voting systems, such as Borda and Plurality) to reverse.
• Maximal disagreement between Borda and Approval is demonstrated in Puzzle 30.

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