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
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
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);
phenomenon that can lead to "chaos";
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;
IRV winner=loser pathology (reversal failure;
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)
of how the Peru 2006 pathology could have
happened under IRV (also same thing happened in
The French study gives an example from real life where
the approval-voting election winner had below 50% approval.
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
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);
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
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).
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";
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.