25
Jan
09

Should I stay or should I go

As promised, our Senior Math Correspondent Alex follows up with an explanation of how it is unlikely that Jeremy Wood dropping out of the race would effect any outcome.

First, a brief explanation about the balloting system being used in this election: Condorcet Ranked-Pairs (hereafter RP).

The huge difference between RP and First Past the Post is the use of ranked ballots, and the translation between a ranked ballot in to a series of candidate pairs. First, voters rank candidates by preference on their ballot (Nader 1, Gore 2, Bush 3). Then, the elections committee turns this ballot in to a ‘candidate pairs count’, which looks like: (Nader, Gore), (Nader, Bush), (Gore, Bush), where bold means ‘beats’ for this ballot. After all the votes are tallied, the elections committee can introduce a ‘weight’ to each win in each pair, for example, Nader beat Gore by 23 (N>G 23), Nader beat Bush by 13 (N>B 13), Bush beat Gore by 8 (B>G 8). After this, the elections committee ranks the pairs, starting with the largest weight, and goes down the list. N>G and N>B are the first two, so N beats both G and B. The third, B>G, means N>B>G, and N wins.

The importance of ordering is in case a contradiction occurs. For instance, say (N>G 31), (B>N 23), (G>B 14). Then we arrive at B>N>G by the first two, but then we have G>B (contradicting the first two together). In RP, we simply disregard those wins of lesser-weight if they contradict wins of stronger-weight. End result: B>N>G. Simple.

So, what does it mean in this kind of a system if a candidate is to drop out/be introduced?

In short, almost nothing. Let us run a hypothetical situation involving three candidates (because four is too much math): Jo, S and Jer. For arguments sake, lets run an election with only Jo and S. Lets say the result is (Jo>S 30). End result: Jo>S (the same as FPP). Now lets keep voter preferences the same, so (Jo>S 30) remains true, but reintroduce Jer. Most of the time, this will not change the end result of Jo>S (with a Jer in there somewhere), but in a rare circumstance, it may flip to S>Jo (as RP satisfies ISDA, not IIA–a shortcoming of the system). The only way for this to happen is to have (Jo>S 30) be a disregarded pair, meaning it needs to be a weak win, relative to the pairs with Jer, and the electorate need to have a circular preference when Jer’s involved. For instance, if(S>Jer 55) and (Jer>Jo 42) were to occur, we would have S>Jer>Jo, because (Jo>S 30) would be dropped.

So, if it is Jeremy’s sole intent to ‘ruin’ Johannes’s chances of winning, acclaiming Sonia as VP A/UA, it is actually in his interest to remain in the race if he believes Johannes is ahead of Sonia. But, the electorate would have to feel very strongly about Jeremy compared to the other two, as they would have to think Jeremy is much better than Johannes, but that Sonia is even better than that.

The trickiness here is symmetric though, and if prior to introducing Jeremy, Sonia is actually ahead of Johannes, it is in Jeremy’s best interest to leave the race.

All in all, the effects of a candidate entering or leaving a race are much, much harder to predict in RP, despite the fact that a candidate may be able to effect the result by entering/leaving a race. This is, without a doubt, a less-strategic situation than FPP would ever yield, as the above analysis is not only unlikely, but also extremely difficult to predict well enough to know whether or not to drop out.

And even then, at the end of the day, if Jeremy is in it to actually win, then it’s obviously in his interest to stick around.

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6 Responses to “Should I stay or should I go”


  1. January 25, 2009 at 12:14 pm

    Epic confusion is right.
    I know how the system works and your explanation only served to compound my pre-existing headache. Alex, do everyone a favour… never, ever write a textbook. Please?

    😉

  2. 2 Ricky
    January 25, 2009 at 3:21 pm

    SOOO CONFUSING!!

  3. 3 radicalbeer
    January 26, 2009 at 2:14 am

    Try harder people. It’s not that rough.

    http://en.wikipedia.org/wiki/Ranked_pairs

  4. 6 Alex Lougheed
    January 18, 2010 at 1:00 am

    Yeah, this reads a lot denser a year later…


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