MN Sen Recount (UPDATE: Stuart Smalley certified winner, lawsuit forthcoming)

[ag]

This is excellent news. I had all but reconciled myself to loss.

It was inevitable and you know it.

Oh no, I really thought he'd steal this one. Fortunately, we stole it instead.

This is one reason to like a runoff system for major races. The revote will usually remove any idea that one side or the other "stole" the election. It also gives the 3rd party voters a chance to decide what (if anything) they want to do with their vote.

It actually creates an extra opportunity for a screw up. First, when the third candidate comes within .01% of the second and they battle it out, who should have gone into the run-off (not that unrealistic in MN, come think of it). And second, when the final result is 50.01% vs. 49.99%

[ag]

I'll agree with you that run-off is better than no run-off but close results are just as likely. That's the point I'm trying to make. The voting method should be a separate consideration from how to deal with close elections. Because we will have these rare, close elections under any system.

What's less likely is two consecutive close races. The assuming equal probabilities at each stage, the combined probability decreases as the square of the probability.

In a plurality system you can't have two consecutive races, so technically it's greater (since it's greater than 0) in a run-off system.

I think you're still looking at this wrong. Yes, if your initial results are:

A: 40.01%
B: 39.99%
C: 20%

Then yes, it is unlikely the run-off will be close. But here's the crux. The chances, on average, of having elections close in the initial tally are balanced, on average, by the chances of having run-offs where the result is close, even though the initial tally wasn't.

I disagree. You assume that all races are equally likely to be close. I assume that races with more than two candidates have a greater likelihood of being close due to the reduced pool of voters for the top two candidates.  With fewer votes the statistical fluctuations that can lead to a close vote have a greater impact. This leads me to fewer close races after a runoff than in a plurality system.

You are forgetting, that run-off would lead to a substantial increase in the number of races w/ more than 2 candidates. In fact, methinks, if the run-off were the norm, the three- or four- semi-serious candidate races would become the norm as well.