[EM] Implicit order, enhancing a method with itself, untying SRP

Filip Ejlak tersander at gmail.com
Mon Aug 14 07:03:27 PDT 2023


Many methods give some explicit order of winners: for example in FPTP there
is an obvious 2nd place for the candidate with the 2nd largest number of
first preferences, etc.

However there's also what I call the "implicit order" of winners (which
might be very different): that's when you eliminate the winner from the set
of candidates, then check who will now become the new winner, then
eliminating them, etc.

Such an order can be used for runoff purposes - eliminate the last place
candidate, then recalculate the order, eliminate the new last place
candidate, and so on, until you have one candidate left. That's not a new
idea - I'm sure I've seen someone doing this with IRV quite a long time
ago. But this can be done with any base method.

In some cases, such a process will produce something entirely different
than the base method - for example, it will transform every non-Condorcet
majoritarian ranked method into a Condorcet one.
In some other cases, it will make no difference at all - like when the
method is LIIA-compliant.

It's closer to the second option with Selective Ranked Pairs - my
simulations suggest that the method is LIIA-compliant unless ties are
involved. Using the self-enhancement process here seems to be a good way to
resolve ties in a monotonic and cloneproof way. It doesn't seem to affect
the high strategy-resistance of the SRP method (which in this respect seems
to look better than Smith//X but not as good as Smith//IRV).
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