[EM] Thoughts on Majority Criterion

[Alex Small]

Several months ago somebody on the list (can't remember who) recommended a
book on the measurement of voting power (can't remember the exact title
either).  They cover a wide range of voting systems, including those where
some voters have unequal weight (e.g. shareholders, electoral college),
those that require a supermajority (e.g. Constitutional amendments in
Congress), and those where some voters have veto powers but not
dictatorial powers (e.g. UN Security Council).

They generally look at an electorate, or set of voters, and ask which
subsets of that electorate are sufficient to enact a resolution.  Suppose
that two winning subsets are called S1 and S2.  If there exist winning
subsets S1 and S2 such that the intersection of S1 and S2 is empty then
they call it an "Improper Voting Game".  If all pairs of winning subsets
have a non-empty intersection they call it a "Proper Voting Game".

They point out the pejorative-sounding "Improper" label is given because
in such a system a resolution could be enacted by a group of voters, and
then immediately after a counter-resolution could be enacted by the
opposition.  This could go on and on, hardly a stable system.

A system in which a minority can enact a policy fits the "Improper Voting
Game" definition.  Hence, one could say that the Majority Criterion is
important in the interests of stability.



Alex


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