[EM] Re: IRV for president: 2 votes overpower 105 million

[Rob LeGrand]

Craig Carey wrote:
>                   Votes                          Percentage
>    +----------------------------------+  -------------------------
>    |  A     50,000,001   199,999,999  |   20.0000004  49.99999975
>    |  BA    49,999,999    50,000,001  |   19.9999996  12.50000025
>    |  CB   100,000,000   100,000,000  |   40          25
>    |  DBA   50,000,000    50,000,000  |   20          12.5
>    +----------------------------------+  -------------------------
>  Winner:             A             B
>  Total:    250,000,000   400,000,000

Or, in the notation I prefer:

 50000001:A>B=C=D
 49999999:B>A>C=D
100000000:C>B>A=D
 50000000:D>B>A>C

and

199999999:A>B=C=D
 50000001:B>A>C=D
100000000:C>B>A=D
 50000000:D>B>A>C

So adding 149999998 A>B=C=D ballots and 2 B>A>C=D ballots changes the
winner from A to B under IRV, which is certainly screwy.  Craig seems to be
saying that IRV is defective because it chooses B instead of A in the
second election.  I'd say that IRV is defective because it chooses A
instead of B in the first election, in which almost 80% of the voters voted
B over A.  B is the Condorcet winner in the second election, so IRV
stumbles upon the correct choice in that case.  Craig's example effectively
demonstrates IRV's caprice, but I think he has the wrong remedy in mind.

--
Rob LeGrand
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/

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