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).
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 ------------------------------------------------------ Secondary Mathematics Assessment and Resource Database http://smard.cqu.edu.au ------------------------------------------------------ Exploring Data http://exploringdata.cqu.edu.au ------------------------------------------------------
----- Original Message ----- From: "Guy Brandenburg" <firstname.lastname@example.org> To: <email@example.com> 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 >