Math Forum Discussions

Rex

Posts: 119
Registered: 12/6/04

Frequent posters to this list.
Posted: Nov 12, 2000 8:14 AM

Plain Text

Correction: Michael Goldenberg hasn't sent 101 messages to the list;
rather, he has sent the same message 101 times.

Ditto Victor Steinbok (65 messages), Domenico Rosa (55 pseudo messages) and
Greg Goodnight (44 messages).

I concede I might be wrong, as I haven't read their posts for a while. All
of these folks are on my Internet Explorer 'block sender' list. At times
they have all written thought-provoking emails, but these days their 'chaff
to wheat ratio' has become intolerably high.

BTW, to block a sender in Internet Explorer 4.0 is easy - open one of his
messages, then click on (Message, Block Sender, Yes).

Cheers

Rex
---------
Rex Boggs
Glenmore State High School Phone: 0749 230 338
P.O. Box 5822 Fax: 0749 230 350
Rockhampton Mail Centre
Rockhampton QLD 4702
Australia
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----- Original Message -----
From: "Guy Brandenburg" <gfbranden@earthlink.net>
To: <math-teach@forum.swarthmore.edu>
Sent: Sunday, November 12, 2000 12:04 PM
Subject: Borda count

>
> Because of the tremendous interest by my students in the recent
> presidential election, I decided on Thursday to scrap the
> previously-planned lesson and instead to do a lesson on voting theory.
> We compared :
>
> * plurality voting (our current system, where the person with the
> greatest number of votes, even if only around 27%, wins -- and that
> happens to be the percentage tallied by the winner in my school board
> district);
>
> * runoff voting, where one takes the top two vote-getters and holds a
> runoff election between them;
>
> * repeated runoff voting, where one takes the lowest vote-getter and
> eliminates him or her, and does a runoff between the remainder,
> repeating if necessary until a majority is reached;
>
> * Borda counting, where the voters give a numerical preference to the
> candidates, and an algorithm of some sort is used to decide how many
> points to give to each voter's first choice, second choice, third
> choice, and so on.
>
> (I mentioned that some countries have instant-runoff voting. Students
> complained about the Electoral College and all of the irregularities in
> this year's election, but that was not the main focus of the lesson.)
>
> I made up an example with four candidates, and the following preferences
> among the following groups of voters. The candidates were Julia, Kate,
> Larry, and Max. From memory, I think I had the preferences as follows:
>
> # of voters first choice second choice third choice fourth choice
> 6 Julia Kate Larry Max
> 8 Max Kate Larry Julia
> 5 Larry Kate Julia Max
> 3 Kate Julia Larry Max
>
> (obviously there are 24 ways of arranging preferences for 4 candidates,
> but I was trying to keep it simple.)
>
> This means that for 6 voters, Julia is the first choice, but they think
> that Max is the worst; and so on...
>
> Max wins the plurality vote, even though 14 of the voters think that Max
> is the worst.
>
> Julia wins a runoff between the 2 top vote getters by 14 to 8, a
> majority, because she gets the votes from those who wanted Larry or Kate
> as their first choice.
>
> In a repeated runoff count, Kate is eliminated from the first round, and
> those votes go to Julia. In the second round, Julia has 6+3=9 votes, Max
> has 8, and Larry has 5, so he is eliminated, and his votes again go to
> Julia, who wins again in the third round, 14 to 8 against Max.
>
> In a borda count, we award 3 points to 1st choice, 2 to 2nd choice, 3 to
> 3rd choice, and 0 to 4th choice.
> So Julia gets 6*3 + 8*0 + 5*1 + 3*2 = 29 points.
> And Max gets 24 + 0 + 0+0=24.
> And Larry gets 6+8+15+3=32.
> And Kate gets 12+16+15+9=52, and wins by a lot.
>
> Notice that Kate was either the first or second choice of all of the
> voters. I wonder how McCain would have done if we used a Borda count?
>
> My students generally concluded that the plurality method we use is the
> worst of the four methods I mentioned, and that the Borda count is the
> best at actually expressing mathematically the will of the people.
>
> No, I did not go into Condorcet voting. I am not of the opinion that it
> is a good way of doing voting. There are too many cases where voters
> will prefer A to B, and B to C, and C to A. Thus we become irrational
> because we are intransitive.
>
> Lani Guinier was blackballed because she proposed a slight variation on
> the Borda count: a voter could cast all of his or her points for 1
> candidate, i.e. calling one candidate your first AND second AND third
> AND fourth AND fifth AND sixth choice if one wants. To me, that minor
> variation is not all that important.
>
> Certainly a Borda count could be handled by voting machines. With a
> well-designed national or state-wide ballot, we could have instructions
> that made more sense than what they had to face in Palm Beach County,
> FL. And clearly there are voting machines that will simply not permit a
> voter to attempt to cast a vote that does not follow the rules, hence
> forcing the voter to re-do his or her ballot until it makes sense.
>
> But it'll never happen. Too bad.
>
> Guy Brandenburg
>
> My souces for this lesson were, more or less, the COMAP book For All
> Practical purposes, which is an interesting source of ideas; columns I
> had read a long time ago in Scientific American by Martin Gardner and I
> suspect others on Kenneth Arrow's apparent proof that the only type of
> election procedure that actually follows a few apparently simple axioms
> is a dictatorship; and a much more recent article on voting theory by a
> person whose name I cannot recall right now because I forgot to bookmark
> it and instead simply printed out and took to school. He contradicts
> Arrow. I will attempt to find this citation on Monday.
>
> GFB
>