Fw: A further elucidation of my arguments

[David Catchpole]

I apologise if this sounds too biased (and I apologise for my previous
misspelling- not my fault, promise!) but I feel you're ignoring the
significance of the example I gave you by making up with a bad contention
of random individuality. Of course, if we took the entire society into
account as is the genuine case with Borda the probabilities you define
would read A:1 , B:1/2.

I see an irrational fear of the inappropriateness of Borda.

On Wed, 21 Apr 1999, Paul Dumais wrote:
> 
> I see an irrational fear of the word "probability". The reason I say
> this is because my model does not at any time choose a ballot at random.
> But perhaps I was not clear enough. The Borda Probability - BP(X) is a
> measure which takes all ballots into account. The only reason its called
> a probability is because the results are normalized. By normalization I
> mean we divide a result by the total number of available votes. Using
> probablty is valid here since it is equivalent to the following:
> Candidates A and B are running. A gets 40 votes and B gets 60. We can
> say that 60% of the people chose B. We could also say that if we choose
> a vote at random, there is a 60% chance that that vote would be for B.
> Notice I said "if". We are not implying that a vote such as this would
> involve actually choosing a ballot at random to select the winner.
> 	Normalization is a good way to compare results of different votes where
> different numbers of voteres are involved. If A and B run again next
> month with 200 voters. If we said B got 65 votes this time we don't know
> how he did against A unless we know how many votes were cast. By
> normalizing we get a useful measure: 32.5% of voters chose B. This is
> iquivalent to P(B) = 0.325 which is the probability that a randomly
> chosen vote will be for B. The only reason I use probability theory is
> that it opens the door to a very well established branch of mathematics
> which can give an analytical breath of fresh air which this discussion
> sorely needs. I think I have explained your paradox using a normalized
> borda count or nanson method. If you have any more questions about
> probabilty, you may save time by consulting a text book.
> 
> > Perhaps the thing that disturbsme most about Borda is that there is no
> > theory to support it which actually reflect any of the reasons a
> > particular voting system is better than another.
> 
> The above statement is only as good as the "reasons" you allude to. I'm
> very open-minded however. I'm am eager to be proven wrong. To summarize,
> I now prefer the Nanson method. It is easy to apply (just rank one or
> more of the eligible candidates). It can be used for multiple seats.
> There are no wasted votes. The result can be converted to a probability
> (call it a ratio if you hate the word "probability") which can be used
> to meaningfully compare elections with varying numbers of seats, voters
> and candidates. I have not encountered an "unfair" result using this
> method.
> 
> Criterions:
> 
> Consistancy: Can someone give me an example of how Nanson fails this?
> GITC: I'm not sure how Nanson fails this iether.
> Monotonicity: This criterion is not required to produce a fair result.
> Since by changing some ballots such that X goes into lower positions you
> put other candidates into higher positions. I'm not sure if Nanson can
> fail without changing the relative postion of other candidates (which
> would make the criterion inapplicable).
> Reverse consistancy: I can't imagine an example where Nanson fails here.
> SPC: This criterion doesn't seem to be necessary for a "fair" result.
> LIIAC: Doesn't seem necessary for a "fair" result.
> 
> Thanks for the lively debate.
> 
> 
> -- 
> Paul Dumais
> 
>