Theorem (& proof) explaining why Instant Runoff Voting (IRV)
leads to 2-party domination (just like under the flawed plurality system it was
supposed to "fix.") Also, shows, remarkably, that the probability of a FBLE
(favorite-betrayal lesser-evil) situation in a random large IRV election
is arccot(√2)/π≈0.195913, albeit arguably 100%, and also
does a similar FBLE analysis for Condorcet voting.
More on this.
Unintuitive examples where
approval-style range voting is not strategically optimal.
But these examples do not occur (i.e. the departure of the best approval-style vote
from optimality is negligible)
in large realistic elections in which 3-or-more-way lead-ties
(and near-ties) are regarded as negligibly unlikelier than 2-way lead-ties.
Unintuitive examples
where dishonest approval-style range voting is strategically optimal.
But this cannot happen in 3-candidate elections, nor can the dishonesty
ever involve your favorite (or
your most-hated) candidate.
Also it in practice in 4- and 5-candidate elections seems rare and has small probabilistic
effect.
Range voting strategy experiments
showing that honesty is actually a pretty good strategy.
Theorem and proofs showing (essentially) that
no pure-rank-order-ballot voting system can obey both the favorite betrayal criterion
and immunity to candidate cloning. But range voting obeys both. More precisely, we give
numerous sets of criteria that range voting obeys but no
pure-rank-order-ballot voting system can obey.
Theorems about point runoff systems: all of them
are non-monotonic, exhibit "no show paradoxes," exhibit "favorite betrayal,"
and disobey consistency with respect to partitioning into districts.
In 2006 Balinski & Laraki proposed
a voting system very similar to range voting. But it is different because based on
medians not averaging. Here is a
critique.
Some simple voting optimality
theorems;
pretty trivial and presumably previously known, although
I have not seen such clean statements before.
But I believe Bayesian Regret
is a better optimality measure than
any of these measures.
Proof that
"participation failure" is forced in Condorcet methods
with at least 4 candidates.
An interesting and simple model of issues and voting
the YN model in which range votng performs optimally (with
honest voters)
while most rival voting methods can perform pessimally or near-pessimally badly.
Criticism of the voting-related work of mathematician Don Saari.
Analysis
of different voting systems vis-a-vis Los Angeles Mayoral Elections.
Analysis
of true versus instant runoffs based on real-life data – true runoff winners
differ from plain-plurality winners over three times as often.
The Romania 2009 presidential
election featured one or more high Condorcet cycles, and the apparent
approval-voting and range-voting
winners officially finished 3rd and/or 6th.