# [EM] STV and weighted positional methods

Kathy Dopp kathy.dopp at gmail.com
Thu Jan 29 11:13:44 PST 2009

```I disagree with your characterization that in your example C does not
have majority support because all 100 voters prefer C over at least
two other candidates,

However, I see your point that the numerical total value of votes
received by C, is not a majority out of the total numerical value of

Cheers,

Kathy

On Thu, Jan 29, 2009 at 1:59 AM, Kristofer Munsterhjelm
> Kathy Dopp wrote:
>>
>> James,
>>
>> Thanks but I don't need to read any references, the arithmetic is obvious.
>>
>> In Borda there can be more than one candidate with majority approval
>> and the candidate with the *most* majority approval may not be the
>> plurality majority winner like it would be in a first round majority
>> winner in IRV.
>>
>> Apparently your definition of majority winner, only includes first
>> choice winners, and that's OK, but then an obvious consequence of your
>> definition is that it compels you to admit that IRV finds "majority"
>> winners far *less* often than a primary/general election or esp. lots
>> less often than top-two runoff.
>>
>> I mean *let's get real* and start telling it like it is.
>
> I think what he's talking about is that Borda can fail to discover a true
> majority. Consider this Wikipedia example, for instance:
>
> 51: A > C > B > D
>  5: C > B > D > A
> 23: B > C > D > A
> 21: D > C > B > A
>
> 100 voters, so A has a majority outright. But the Borda scores are (when
> 0-based):
> A: 51 * 3 = 153
> B: 51 + 5 * 2 + 23 * 3 + 21 = 151
> C: 51 * 2 + 5 * 3+ 23 * 2 + 21 * 2 = 205
> D: 5 + 23 + 21*3 = 91
>
> so C wins.
>
> Borda can still be interesting, because its single winner elimination
> versions (Nanson and Baldwin) pick from the Mutual majority set. The
> multiwinner equivalent of mutual majority is Droop proportionality, so it
> would be of interest to see if Borda-"STV" would be proportional. I don't
> think it would be (given my Left-Right-Center example in another post), but
> how far does it fall from the mark, and why does plain old STV pass it in
> that case, given that Plurality itself doesn't pass mutual majority?
>
> Of course, if I could find a reweighting scheme that works for any WPS, the
> generalized/altered STV doesn't have to use Borda; it can use any weighted
> positional system, and even some that are not (like Range).
>

--

Kathy Dopp

The material expressed herein is the informed  product of the author's
fact-finding and investigative efforts. Dopp is a Mathematician,
Expert in election audit mathematics and procedures; in exit poll
discrepancy analysis; and can be reached at

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Post-Election Vote Count Audit
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http://electionmathematics.org//ucvAnalysis/US/paper-audits/Vote-Count-Audit-Bill-2009.pdf

History of Confidence Election Auditing Development & Overview of
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http://electionarchive.org/ucvAnalysis/US/paper-audits/History-of-Election-Auditing-Development.pdf

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