[EM] random eg w. improved version of IRV3.

[David L Wetzell]

I took Warren's example and ignored all of the voter information except the
top 3 choices, tallied up (with Excel) the number of votes each got so that
A, B and E were identified as the finalists.  I then sorted each of the
votes into one of ten categories based on preferences between the three
finalists and then summed up the number in each category.  Only two voters
didn't have one of the three finalists in their top three.  I added
together the three categories for each of the three finalists, where they
were the top preference among the finalists.  The totals were: A: 11, B:
14, E:10.  This eliminated E so that 3 votes were transferred from E to
each of the two candidates, which made B beat A, 17 to 14.   But let's say
E demanded a recount and instead we considered the outcome if we eliminated
A instead.  Then B would beat E, 20 to 12.

So B wins, almost with a majority, which isn't bad with 7 a-priori
competitive candidates, an assumption that is not realistic for real-world
important single-winner
elections.  And, 43% of the vote information was used, the lower rankings
were not important and so their non-usage is not important and would be
robustly not important if the number of competitive candidates tended to be
relatively low for a variety of real world economic(cost of campaigning,
building name recognition), psychological reasons(short-cuts used by
rationally ignorant voters with opportunity costs to the time spent on
politics).

dlw
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