kitchen table math, the sequel: help desk

## Friday, May 4, 2007

### help desk

We have a 3-way race for board.

Two seats are open; voters can vote for two candidates.

How do you maximize the chances of one particular candidate winning?

Do you vote only for that candidate?

OR: say you think your candidate is least likely to win --- and you think you know which candidate has the most support.

Say there's one candidate you absolutely don't want on the board (and by the way, that's not the case here -- Ed and I like all 3 candidates & have been debating which two we'd prefer) -- but say you have a candidate you absolutely don't want on the board, then what?

The scenario of having one candidate you absolutely don't want, btw, does hold true for some voters here. I would go so far as to say that, of people who are tuned in, Ed and I are the only people who don't harbor a passionate objection to one candidate in particular.

We're perplexed.

Doug Sundseth said...

In a race of this sort, what is important is not the total number of votes, but the relative number of votes. You want to increase or decrease the votes of the appropriate candidate(s) relative to all other candidates. So:

If you want only one particular candidate, vote only for that candidate. If you want to stop one candidate, vote for both his opponents.

In each case, you've provided a delta of one vote relative to the rest of the field, which is the best you can do legally.

Doug Sundseth said...

I should probably note that the analysis gets a bit more complicated when you have (say) four candidates for two seats. The "one guy you like" analysis stays the same, but voting against someone is more difficult.

In that case, you need to identify the bad guy's most probably successful opponents and vote for them.

LynnG said...

Is the one guy you don't like from the same party as one other candidate, or is he/she the only candidate from that party?

If you really like one candidate, the best strategy is to make sure they are not alone from their party.

If you are the lone candidate, it is really impossible to get people to throw away one of their votes, so you have to get someone else to run from your party. Then you will at least capture all of your party's voters without "losing" the 2nd vote to your opponents.

I think the 2 against one setup is weighted heavily against the loner.

Independent George said...

Kenneth Arrow won a Nobel for studying this problem; unfortunately, I believe he concluded that the problem was insoluble.

*This was actually a source of great amusement to my 16 year-old self. "Hey, Mr R - I can't solve this question on your exam. When do I get my Nobel?"

Independent George said...

Yep - once again, the Googoracle at Wiki knows all: Arrow's Impossibility Theorem.

Unknown said...

Yeah, we have school board candidates on the upcoming primary ticket. Considering the crap the current school board has been pulling, I'm voting for whoever the challengers are.

TurbineGuy said...

Vote for Bob Roberts...

Rudbeckia Hirta said...

I think that what Arrow showed was that it's impossible to design a "perfect" voting system with more than two candidates.

What this means is that any system with more than two candidates has flaws, and if you're lucky you can exploit them to your advatage. :)

Once at an MAA meeting I went to a talk by a guy who does voting theory and quipped that he was available as a consultant. He says that if you give him poll data and tell him who YOU want to win, then he can design a seemingly-fair system where your candidate will win.

Catherine Johnson said...

Once at an MAA meeting I went to a talk by a guy who does voting theory and quipped that he was available as a consultant. He says that if you give him poll data and tell him who YOU want to win, then he can design a seemingly-fair system where your candidate will win.

absolutely

I'll get Ed to tell me what happened in France....can't remember it off the top of my head

They made some reform requiring that women be elected.

Game theorists told them before they even did it how people would game the system (word rep!)

They predicted exactly what people did

Catherine Johnson said...

There are no parties in this case.

Someone -- either the administration or .... supporters of the administration (?) .... attempted to block one of the three by convincing the other 2 to run as a ticket.