Week 11… Just Checking In
Posted on: April 30, 2011
Here we are… down to the wire. I can hardly believe I am scheduled to present my Capstone project a week from today! I expect to finalize the second draft of my paper tomorrow, so I can begin to put together the slides for my presentation. I have the notes I need, my professor is helping me with the graphics and outline, so now, in the words of that ever-popular motivational Nike ad, “Just do it.”
I met with my professor yesterday about Capstone, and as usual, he made sense out of the obscure… I am so grateful for him!! He helped me understand where my paper needs to go in order to bring the information I have so far to its logical conclusion. I will be working on the last few sections of my paper this weekend, and then I should be ready to start putting together my presentation. At least, that’s the plan!
Week 9… Break? What Break?
Posted on: April 16, 2011
Spring Break has come and gone, and I spent a good part of it doing an assignment for one class (that was due the Friday of Break, if you can believe that!!!), studying for the mid-term in another class, and writing the rough draft for my Capstone. I got the assignment done on time, I did well on the mid-term exam on Tuesday, but I only managed to complete about 75% of the Capstone paper by Wednesday’s deadline. I am really grateful for the time I had to work on it, but I was quite disappointed that I didn’t manage to get it finished. I tried hard, but I just wasn’t able to pull it off.
It is critical that I complete the final sections of the paper soon, because I must begin focusing my attention on preparing for the presentation I will be giving in early May. To that end, I will be working to gather as much information as I can about Donald Saari’s analysis of election outcomes. I’ve laid the foundation in the paper, now I need to try to bring it to its logical conclusion… as soon as I determine what that is! So here we go, more reading and (hopefully!) more writing.
Week 8… Let the Writing Begin
Posted on: April 2, 2011
Spring Break has arrived, and I will be using this time to write the first draft of my Capstone paper that is due the Wednesday after we return to school. I met with my professor this past week to get some much-needed direction, and he showed me how to use concepts I learned in Linear Algebra to find and look at election results. For a 3-candidate election, a 3 x 6 matrix can be used to transform a voting profile vector from 
Week 7… Focus, Focus
Posted on: March 26, 2011
In creating my outline last week, I began to suspect that my initial goals for Capstone were a bit too ambitious. There is so much interesting material that could be covered, but in order to include everything I wanted to, I would practically be re-writing Mr. Saari’s book. Since that is not an option – for a multitude of reasons – I realize now that I need to narrow my focus in order to do justice to the topic. I will be meeting with my professor this coming week to get some direction on refining my goals, so that I will know how to proceed when I begin writing my rough draft during spring break.
Week 6… Confession Time
Posted on: March 19, 2011
It is time to report on my progress, but I am sad to say that I have none to report! The truth is, I have not been able to work on my Capstone project at all this week. Even though it has been on my “to do” list each day, it just has not happened. However… the preliminary outline for my paper and presentation is due tomorrow, so I’d say it is pretty clear what I will be doing between now and then!!
Week 5… Marching On
Posted on: March 12, 2011
I am continuing to read Chaotic Elections, and I still find this entire subject of “elections gone wrong” quite fascinating. How can something we often take for granted wreak such havoc in our lives – without us even realizing it is happening? And then when “we” think we have found a wonderful strategy to bend an election in “our” favor, we create another whole set of problematic outcomes. Amazing!
So far, the book has been part history lesson, part civics lesson, part statistics, and a fair amount of surprises. Donald Saari does a great job of putting the voting paradoxes in terms that can be easily understood, such as using allegories to school grades and class standings for various voting methods, before he gets to the actual mathematics he used to analyze them. His mathematical analysis will be the meat of my Capstone presentation, but I also intend to use some simpler examples to aid in understanding.
This week I will be working on the outline as I continue to read Chaotic Elections, all the while referencing my linear algebra textbook, as needed.
Week 4… More of the Same
Posted on: March 5, 2011
I am afraid this update isn’t much of an update, in that it really doesn’t carry much by way of new revelation. I am continuing to ready Chaotic Elections, but it is going more slowly than I had hoped. My biggest challenge is carving out time to read, and then when I do, it is not the kind of material I can just breeze through and “get it.” The subject is very interesting, and I am learning a lot and enjoying it immensely. I am concerned, however, that I will have trouble keeping up with the Capstone timeline… the outline is due soon. Pesky things keep getting in the way – things like other classes, if you can imagine that!!
My goal is still the same, to continue reading the book and refining my outline.
Week 3… Pressing Onward
Posted on: February 26, 2011
On Wednesday I met with my faculty liaison, Dr. Edgar, about my Capstone project. He encouraged me to continue reading Chaotic Elections with an eye for linear algebra. Donald Saari uses vectors, specifically what he calls voting vectors, to analyze the various voting methods, do manipulations of outcomes, and support his argument that the Borda Count is the superior voting method whenever three or more candidates or issues are on the ballot. My goal for this week, then, is to continue reading and refining my understanding.
Week 2… Good Intentions
Posted on: February 19, 2011
Although I did not get to read Chaotic Elections as much as I had hoped (I did read a little), I have begun to formulate ideas for my Capstone outline. These are my first thoughts:
1. Define voting paradox and explain election conditions that may be problematic, i.e., there are three or more candidates or issues on the ballot, and the winning candidate or issue does not receive a majority of the votes.
2. Define various voting methods: plurality, Borda Count, Condorcet.
3. Offer brief historical background: Borda, de Condorcet, Arrow, Saari.
4. Give simple example to demonstrate the three voting methods and how different methods can produce different results when applied to the same election.
5. Explain some of the voting biases inherent to each of the methods, with examples, and the kinds of fallacies that can result.
6. Discuss how Donald Saari used mathematics to identify specific kinds of voting paradoxes, to analyze each for the causes of the various voting biases, and to determine the most reasonable voting method, i.e., the one most immune from voting method biases.
7. Offer possible reasons why, in light of existing evidence, wholesale changes have not yet been made to elections to insure that outcomes accurately reflect the will of the people
I will need much more research before I am ready to finalize my outline, and continuing research will be my plan for the week. I will refine the outline as I go, using this rough draft as a starting place.
Pressing Toward the Prize 