[EM] Dollar example

Bart Ingles 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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