Here is some discussion on full and approximate compatibility with
election method related criteria. My aim is to prove that sometimes it
is better to fail to meet some criteria (that are good in the sense
that one wants to meet them) than to meet them.
First a story from real life. A mother of three children buys three
cakes for the kids on her way home. She puts the cakes on the dinner
table for the kids to eat. But then their dog steals and eats one of
the cakes. All the kids try to grab one of the cakes and make sure
that at lest they will get their share. The mother interrupts the kids
and decides to cut the cakes in parts so that each kid gets 2/3 of a
cake. The wrong solution would have been to meet the requirements of
two of the kids. The best solution was not to meet the requirements of
any of the kids.
Let's say that there are three different criteria that an election
method should meet. They are related to three different strategic
voting related problems. As in the world of security also election
methods are as vulnerable to strategic voting as their weakest link.
In this situation there may be a solution that almost meets all the
three criteria but does not meet any of them fully. That solution is
often (but not always) the best solution.
So, there are patterns where a good method should meet only a strict
subset of the requirements that some competing methods meet. One may
thus improve a method by making it incompatible to some (good)
criterion that it earlier met. The point is that compatibility with
various criteria should often not be an on/off comparison but a richer
analysis where also partial and almost complete compatibilities are
counted.
Juho
P.S. Note that there are also criteria that one should meet in most
situations but that in some special situations should not be met. A
good method may sometimes fail these criteria, but not to give up
something in order to give space to meeting better / more accurately
some other criteria as discussed above but to directly improve the
method.
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