Date: Nov 12, 2000 8:14 AM Author: Rex Subject: Frequent posters to this list. 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

>