# Re: IRV - was Ms. Tobi's overheated rhetoric

From: Arthur Keller <voting_at_kellers_dot_org>
Date: Mon Nov 12 2007 - 12:11:14 CST

At 7:12 AM -0800 11/12/07, Danny Swarzman wrote:
>Let's consider 12 candidates. That's what we had for mayor in SF last
>time.
>
>How many combinations is that? I get 1453.
>
>Here's how I figure it.
>
>The number of completely filled ranks is the permutations of 12
>things taken 3 at a time, 12! / (12-3)! or 1320.
>Since all ballots with 2 ranks filled are equivalent, there are 12! /
>(12-2)! such possibilities or 132.
>And there are 12 possibilities with one choice marked or 12
>And one empty or 1
>
>1320+132+1 = 1453 combinations.

Actually 1320+132+12+1 combinations = 1465. (I had a typo of 1265 in
an earlier message.)

>How big is the tally sheet now.
>
>If there were 20 candidates, there would be 6840 possibilities for
>completely filled ballots, plus some for partially filled ballots.
>
>The number 12 comes from San Francisco's last mayoral contest. I
>think that last year there were 22 candidates for one of the
>supervisor positions.
>
>A limited number, but an unwieldy number. If you follow the language
>of SF's charter, the elections board could choose to offer more than
>3 ranks. If 3 ranks is more democratic than 1, maybe 10 is more
>democratic than 3. Want to try those numbers?

No, I don't. ;-)

>-Danny

Best regards,
Arthur

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Received on Fri Nov 30 23:17:18 2007

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