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7 candidates, 3 ballots

April 20, 2007
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Sometimes I like running little experiments—simulations, games, activities—in my classes. I think they’re useful to illustrate a point, or to dissect an argument, or even just to make complex ideas more accessible (and fun). This week I roped another six faculty into my latest project: presidential voting simulations.

I was interested to demonstrate the effect of electoral systems on party systems (such as “Duverger’s law”) & electoral behavior to my comparative politics students. In the past, I did a similar simulation at Western, but there I had more than 50 students. W/ only 29 students (and that’s if everyone came), I faced a serious “small-N” problem. Fortunately, six of my colleagues agreed to help.

I selected three different electoral systems that can be used in single member district (SMD) elections. So these are all essentially “plurality” systems—none are proportional representation systems (so, no, I wasn’t testing Duverger’s law). The three systems were:

1. Alternative vote (AV): Under this method, voters are given a list of candidates & must rank order their preferred candidates (“1” is most preferred). If no candidate wins a simple majority (50%+1), then the candidate w/ the fewest votes is dropped out, and his/her votes are transferred to the next preference. This is repeated until a candidate has a majority.

2. Two-round system (TRS): This is a simpler system. Voters cast a vote for one (and only one) candidate. To be elected, the candidate must win a majority; if no candidate wins a majority, then a second “runoff” election is scheduled between the top two candidates.

3. Ley de Lemas: This is a unique system. Voters are given a list of candidates, but the candidates are listed by party. Again, voters cast one (and only one) vote. But it’s not necessarily the candidate w/ the most votes that wins: the winner is the top candidate from the party that won (all together) more votes than any other party.

I ran the elections (doing all three elections took about 5-7 minutes in each class) in eight classes (one of my colleagues let me into two of her classes). And I’ve finished tabulating the votes (as you can imagine, the AV votes can take some time to count). The results are interesting:

In every electoral system, Obama wins (although he doesn’t win in every election in every class). But the numbers are different.

Under AV, Obama wins w/ a staggering 61.2% over Giuliani’s 38.8% (though Obama started w/ only 33.7% before the first vote transfers).

Under TRS, Obama wins a plurality (but not a majority), w/ a decent 36.0% over Giuliani’s 25.1% (McCain and Clinton were close w/ 14.9% & 14.3% respectively).

Under Ley de Lemas, the Democrats won 55.5% of the total vote, and Obama won 31.3% of the total vote (and 56.4% of the Democratic vote).

Clearly, it seems that Obama is the “Condorcet winner” among the 175-182 (the numbers for each voting system varied, since students arrive late to some classes) political science students at Dickinson College.

You’re welcome to look at the data, or to use the ballots I designed. Both files are available at: http://users.dickinson.edu/~centellm/sims/voting/

Hopefully, I can run this again w/ a larger sample (and tossing in some “third party” candidates) in the Fall. My goal is a 1,000+ sample.

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Comments

They are actually doing a simulation like this in Bhutan this week. The goal is to move from a monarchy to democracy.

Posted by jonathan April 21, 2007 8:53 PM

    I’d love to hear more about this. Any links?

    Posted by mcentellas April 21, 2007 11:01 PM

      I'm not surprised; much of the earlier organizing I've come across is for Obama. He has large segments of the college vote (anti-War sentiments).

      Self-selection bias could be a problem. But you could treat counting votes in each class as repeated sampling, no?

      Meh. Econometrics is ruining the way I think. Now back to 2SLS and IVE.

      P.S. - I just noticed...the admin of the Wikipedia Facebook group has deleted all comments. WMU alums too much for the Ivy-leaguers?

      Posted by David April 23, 2007 12:01 AM

        David:

        You’re right, I should’ve treated each class as a new random sample, and then done some sort of probit analysis or something like that. Instead, I just assumed that each sample was random, and that any repetition (some students participated more than once) was also randomly distributed. So I more or less treated the entire group as a sample w/ subsamples. Not ideal for a real experimental-research design, but good enough, I think.

        But, yes, there is clearly some bias in the responses. Since I only sampled political science courses, there was probably some selection bias involved. Although not as much as I would’ve expected. The class on gender & politics didn’t go for Clinton, as I would’ve expected.

        And, yeah, I’m not sure what’s up w/ the Wikipedia group. I think they didn’t like being reminded that you’re not supposed to cite phonebooks and other sources of “general” information.

        Posted by mcentellas April 26, 2007 8:05 AM


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