This entry will focus on my recent reading habits and related thoughts, the topic I found easiest to write about. While there will be little relating directly to Chile, I hope my readers will find something of interest. Future posts will deal with my end-of-semester thoughts comparing the teaching environments at Rhodes and the University of Talca, the research I have done in Chile and my experiences presenting it in New Zealand, and events surrounding the visits of friends and family.
I recently finished reading a fine book called They Marched into Sunlight, by David Maraniss, which is about two nearly simultaneous events that took place in October of 1967. The first is a battle in Vietnam in which American forces were ambushed and sustained heavy casualties. The second is a protest at the University of Wisconsin at Madison against the right of Dow Chemical, manufacturer of napalm, to recruit on campus. The protest turned ugly when the university’s administration, which was relatively sympathetic to the protests, summoned the Madison police, who then used batons and tear gas to break it up. These stories are told with an emphasis on the people who lived the encounters.
Additional context is provided by summaries of the American political scene at the time, with descriptions of Kissinger, Johnson, and, interestingly to me, John Shelby Spong and his role in protesting the draft. Spong recently spoke at Rhodes College, where I teach. Dick and Lynn Cheney are also mentioned as students at UW at the time of the protests.
I came away from this book with an overwhelming sense of sadness and sympathy for the people who were there, particularly those who got swept up into the war almost by accident. The political machines on both sides of the war had entrenched positions, did not trust each other, and were unwilling to meet halfway. It reminds me a great deal of the political situation in the United States today, with one notable difference being that today's protest movement is less visible. As one who has only the remotest and most isolated recollections of the
Related to those crucial virtues, I am now reading books and articles about the mathematical aspects of voting. These include Chaotic Elections and Decisions and Elections, both by Donald Saari, Approval Voting, by Steven Brams, and several related articles. The basic question is, how should a collection of voters choose between a number of candidates?
In the
For a number of years I have been concerned that the plurality method, along with the two party system, encourages voters to split into two camps which may not accurately reflect the complicated political makeup of our electorate. The two sides then wage a vicious battle to see which can eke out a slim victory over the other. The victors spend the next four years advancing their agenda, usually with as little compromise as they can get away with. The ultimate result is further polarization. In other words, the plurality method causes us to shun consensus candidates who might have a chance at crafting unity in favor of those that further our divided condition.
There are other problems with the plurality method. Specifically, many people feel that they cannot vote for their true top choice because they fear that this candidate has no chance of winning. The plurality method causes some voters to lie! Perhaps the most well-known example took place in 2000, when many Nader voters cast their ballots for Gore, their second choice. Another problem is that a person that is considered unqualified by nearly 2/3 of the voters can be elected to office. A recent example is the election of Jesse Ventura as governor of
These instances suggest that there are fundamental structural problems with the way we vote that extend beyond the more superficial issues of close elections, election fraud, denial of voting rights, hanging chads, and malfunctioning voting machines. The superficial issues have received a great deal of attention, while the fundamental issue has received almost none.
So what should we do about these problems with the plurality system? My opinion, which is shared by many experts on voting, is that we need to find a different method to elect our representatives. How can we choose the best alternative system of voting among literally infinitely many possibilities?
In an election, each voter has a preferred ranking for the candidates. The goal is to use these rankings to decide on a collective or societal ranking in a fair way. Some commonly discussed alternative voting systems include:
- approval voting, in which each voter votes once for each candidate she considers to be acceptable. The candidate with the most votes wins.
- the Borda count, in which each voter's top candidate gets n points, the next gets n - 1, etc., the bottom candidate gets 1 point. The candidate with the most points wins.
- Condorcet methods, which say that if a majority of voters prefer A to B, then the outcome should rank A above B. A problem with these methods are that it sometimes leads to situations where A is prefered to B is prefered to C is prefered to A. Various methods are used to resolve such conflicts.
- antiplurality voting, in which each voter votes for everyone but her least favored choice. The candidate with the most votes wins.
- instant runoff voting, in which a candidate with a majority of first place rankings wins. If no such candidate exists, then the candidate that is ranked first by the fewest number of voters is eliminated and the process continues.
One of the goals of voting theory is to discover which of these and other voting systems are well behaved. For example, if everyone agrees that candidate A is better than candidate B, then the collective ranking should put A above B. Also, if society collectively prefers A to B when C is in the race, then society should also prefer A to B if C should drop out. Unfortunately, Arrow’s theorem says that when there are more than two candidates, the only voting system which satisfies the two properties above (assuming some technical but highly reasonable requirements) is a dictatorship! That is, the societal ranking must be equal to that of some voter.
Saari claims to have found a new way to look at Arrow’s theorem to make it seem not so terrible. He favors the Borda count. Steven Brams favors approval voting. Brams recently spoke at Rhodes at the invitation of the math department. He has tried to persuade governments at various levels to abandon the plurality method.
I hope to design and teach a nonmajors course on this subject after I return to Rhodes. I think it may have interdisciplinary appeal, particularly if I can find something positive to say. That is, I feel the course ought to be about more than all of the things that can go wrong with the various voting systems, which is the focus of most of the reading I have done so far.
When I was in Auckland, I happened across a highly accessible book entitled Mathematics and Sex. Its goal is not to teach mathematics but to teach about the many ways mathematics can be applied to the unlikely subject of heterosexual sex. The author, Clio Cresswell, discusses topics including:
- the use of systems of differential equations to model the attraction between a man and a woman when, for instance, the man becomes more interested in the woman when she shows more interest in him and when she becomes less interested in him the more interest he shows in her.
- the optimal number of partners a person should try before finally settling down in order to find the “best” mate possible.
- the “bonk rate”, as she calls it, how it varies over time for a given couple, and how best to model it.
- how the large number of questions asked by dating services leads to what she calls “the curse of dimensionality”.
- how a collection of men and women should pair up according to their lists of preferences so that the resulting pairing is stable, i.e., so that there are no two people of opposite gender that would prefer each other to their current partners.
My biggest complaint is that the mathematics is not adequately developed. For example, equations often appear in which the variables are not defined. This happens frequently enough that it is clear that Cresswell has made a conscious choice to sacrifice mathematical clarity for broad accessibility. Though I found her choice distracting at first -- it makes the equations seem to be plunked down out of nowhere -- I later came to agree with it, since her goal seems to be to bring the appreciation of mathematics to the widest possible audience. Furthermore, she provides references for the material she presents, making it possible for the interested reader to obtain all the detail she desires.
Cresswell writes simply and with humor, making the book entertaining, and speaks frankly and directly, even including some personal revelation. I was impressed by her courage as I tried to imagine offering a course at Rhodes based on her book. I realized I would find it extremely uncomfortable to lecture on some of the subjects she covers. Repeated discussions and cautions of what is and is not acceptable conversational material between student and professor has made me view any mention of sex in class as a third rail.
As a consequence of my fears, I found myself reluctant to give a potentially valuable topic further consideration. It was at this point that I realized that I was engaging in self-censorship that had crossed the line between treating my students with respect and protecting them from any content that might be offensive or uncomfortable, even if it is intellectually worthwhile. This is truly a modern academic hazard.
A tangential consequence of my recent reading has been some reflection on how best to genderize generic personal (possessive) pronouns. For example, when referring to a voter, is it better to say “his preferences”, “her preferences”, or “his or her preferences”? Some social critics have complained that the default use of “he” and “his” does not reflect the reality that women are also participants in society and may lead to under representation of women in some important roles. They have called for a more equitable convention . Unfortunately, the most commonly used "his/her" solution is horribly clumsy and I find myself engaging in literary contortions trying to avoid it.
My solution is for male writers to use female pronouns and female writers to use male pronouns. This convention has the advantages of being linguistically elegant, courteous, and self-balancing. If, for instance, females are over represented in a discipline and if the use of male pronouns encourages males to enter that profession (an assumption that needs empirical support), then the tendency over time with this approach will be towards equal representation of the genders. If certain simplifying assumptions are allowed, this statement can be proved using systems of differential equations! Now you know why I have been using feminine personal pronouns in this blog entry.
More soon. Thanks to those of you who have written to me with comments on previous entries. Your comments are always appreciated! Also, I made a short entry prior to this one that I never sent an email alert about. I had intended to add to it but never did, and upon re-reading it, it seems that at this point it is best to leave it as is. So, if you haven't seen it, give it a look.
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