[EM] Cardinal forms of majoritarian criteria

[Closed Limelike Curves]

A while back, Warren D. Smith made the interesting observation that score
voting satisfies a natural generalization of the Condorcet criterion: any
candidate who would pairwise-beat every other candidate in a one-on-one
race, must win the election.

This leads to the question, are there other natural generalizations of the
majoritarian criteria (e.g. majority, mutual majority, or Smith)?

Smith is easy: because we have a total order over the reals,
there's always a cardinal-Condorcet winner, so it reduces to the
cardinal-Condorcet criterion.

Majority can be extended too, if we think of a majority winner as a
"super-Condorcet" winner. Define a majority winner as someone who could
defeat every other candidate *put together *in an unholy Voltron-style
mashup. We define X to be a majority winner if they could defeat a new
candidate, X', who equals the "sum" of all other candidates. With ordinal
ballots, we take sums of candidates by taking the minimum rank of each
candidate (as in tropical geometry).

Score voting satisfies the same criterion, where the natural sense of
adding two candidates is adding their scores: if one candidate has more
points then every other candidate put together (i.e. a majority of all
points assigned by voters), they're guaranteed to win.

Any other natural redefinitions?
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20240210/f3df1c5b/attachment.htm>