[EM] Dollar example
bartman at netgate.net
Wed Feb 23 01:40:13 PST 2000
This was not intended to address any particular method. Instead, this
deals with standards for who actually _should_ win. There was a debate
recently about whether the CW was always the better choice for society,
or whether some consideration should be given to social utility.
* * *
A community is trying to decide how best to distribute a windfall of
$75,500. There is a dispute over how much each member deserves. Group
A wants to give each of its own members $1000 for every $500 that each
non-member receives. Group C wants the opposite. Group B wants to give
each member of another group $550, and distribute the rest among its own
Group A and C are each close to half of the population, with group B
only a small minority. Exact populations are unknown.
~50 A($1000) B($550) C($500)
~1 B($20500) A=C($500)
~50 C($1000) B($550) A($500)
Converted to vN-M utilities, we have:
~50 A(1.0) B(0.1) C(0)
~1 B(1.0) A=C(0)
~50 C(1.0) B(0.1) A(0)
Since A and C are in a dead heat, it is clearly in those voters'
interest to truncate and accept the AC lottery rather than settle for
the $50. Note that this strategy doesn't depend on cooperation between
the A and C groups -- if either group votes sincerely B wins, so there
is no penalty for using the strategy unilaterally.
It is hard to see how a win for B would benefit society as a whole,
since it mainly concentrates wealth into the hands of a small minority.
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