[EM] STV when applied to choosing pizza toppings

[Nathan Larson]

Does anyone have any comments in reference to this critique of STV as
applied to choosing three pizza toppings? The issue is whether it's fair to
transfer the surplus votes from the winners before transfering votes from
the losers.

---
What you describe would indeed work, however....

Suppose the second choices of the 100 "winner" (pepperoni) votes were
one half for mushrooms, one half for onions. This, if I follow the
numbers correctly, means that mushrooms and onions would win (with 40
and 56 respectively). But look: you have completely ignored the second
(and third) choices of the folks who didn't vote for pepperoni as first
place. You just disenfranchised 56 voters. Why should only the
pepperoni-first voters be the ones who get to exercise their second and
(possibly) third choices? Doesn't seem fair to me! Those 56 NAP
members who didn't vote pepperoni first may ALL have voted (yuk)
anchovies as their second choice. Clearly that would exceed the quota
and anchovies would have garnered MORE votes that any of the
non-pepperoni choices. But you trashed them. For shame!

With smaller numbers the problems become more apparent. I am taking the
liberty of e-mailing you directly the essay I did some years ago.
Enjoy! Meanwhile I'll think about constructing a counter example where
there is no choice but an arbitrary choice (following your rules) that
causes a different outcome.

But not tonight. Too late.


John

John D. Stackpole, CPP, PRP Voice: 301.292.9479
Parliamentary Services Fax: 301.292.9527
11 Battersea Ln.
jstackpo at ...<http://groups.yahoo.com/group/parliamentary/post?postID=xw41E4KqB3bUn6EQv3C5zKpbwJbdHG1w5_E542bKCkoccVRVKuKVRqpWK9yFpoHQOaZP0bOSDstogSXOpQc>
Ft. Washington, MD 20744-7203



Nathan Larson wrote:
>
> Here is an example to illustrate how surplus votes would be transfered
> proportionately under STV. Suppose a state's NAP convention wants to
> order an extremely large pizza, but the coupon only allows three
> toppings. In accordance with the bylaws, everyone submits their
> preferential ballots and the tabulation is conducted using STV. The
> first choices are as follows:
>
> Pepperoni: 100 votes
> Onions: 26 votes
> Green peppers: 20 votes
> Mushrooms: 10 votes
> Anchovies: 0 votes
>
> The Droop quota is [Votes / (Toppings + 1) + 1], which simplifies to
> [156 / (3 + 1)] + 1, or 40.
>
> Pepperoni, with 100 votes, meets the 40-vote quota, so it is declared
> elected, and there are 60 surplus votes. Suppose that for the 100
> voters who picked pepperoni as their first choice, their second
> choices were as follows:
>
> Mushrooms: 50 second-choice votes
> Onions: 25 second-choice votes
> Anchovies: 25 second-choice votes
>
> The 60 surplus votes for pepperoni would be distributed
> proportionately, as follows:
>
> Mushrooms: +30 votes (50% of 60)
> Onions: +15 votes (25% of 60)
> Anchovies: +15 votes (25% of 60)
>
> The standings would then be as follows:
>
> Pepperoni: 40 votes (elected)
> Onions: 26 + 15 = 41 votes (elected)
> Green peppers: 20 votes
> Mushrooms: 10 + 30 = 40 votes (elected)
> Anchovies: 0 + 15 = 15 votes
>
> The decision, then, would be to buy a pizza with pepperoni, onions,
> and mushrooms. The surplus votes were transfered taking into account
> the second choices of everyone who chose pepperoni as their first choice.
>

-- 
Nathan Larson, CPA
(H) 540-788-4945
(C) 703-298-3838

-- 
Nathan Larson, CPA
(H) 540-788-4945
(C) 703-298-3838
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