In a multi-winner election, how many should I vote for?
November 3, 2014 8:15 PM Subscribe
Mathematically, in a 6-way race with 5 winners, should I vote for the 2 candidates I like, or all 5 who I don't hate? Details inside.
There is a local race with 6 candidates, 5 of whom will take office. There are 2 candidates I actively like, 2 I actively dislike, and 3 I don't feel strongly about either way. I have no idea of the relative chance of any of the candidates to win, apart from an impression that one of the "eh" candidates who has been in office for over a decade is likely to continue to be in office. I can vote for up to 5 candidates. Mathematically, would I be more likely to have the most positive influence toward my A)Ideal situation, where one of the two candidates I dislike is the one who doesn't take office and B)Not a total lose situation, where the candidates I actively like both get on if I 1)Vote only for the two I like or 2)Vote for all 5 who I don't hate?
There is a local race with 6 candidates, 5 of whom will take office. There are 2 candidates I actively like, 2 I actively dislike, and 3 I don't feel strongly about either way. I have no idea of the relative chance of any of the candidates to win, apart from an impression that one of the "eh" candidates who has been in office for over a decade is likely to continue to be in office. I can vote for up to 5 candidates. Mathematically, would I be more likely to have the most positive influence toward my A)Ideal situation, where one of the two candidates I dislike is the one who doesn't take office and B)Not a total lose situation, where the candidates I actively like both get on if I 1)Vote only for the two I like or 2)Vote for all 5 who I don't hate?
I count 7 candidates in your breakdown, btw. I'd agree with Jairus that it depends a lot on what method is used to determine a winner, however, I'd say that regardless of the system it's generally going to be more likely that your good and meh candidates win over the candidates you dislike if you vote for all of the ones you don't hate. People don't get elected if no-one votes for them.
posted by Aleyn at 8:21 PM on November 3, 2014
posted by Aleyn at 8:21 PM on November 3, 2014
Response by poster: The top two vote getters in each district, then the 5th seat is an "at large" seat, which, I assume, will go to the remaining candidate with more votes.
And now, looking at my list, I see that I miscounted (Oh, for Pete's sake, Debet, honestly). There are 7 candidates.
I can vote for 3 in my home district and 2 in the other, which aligns with the 5 votes I would place for option 2. The two I really like are in different districts.
posted by DebetEsse at 8:22 PM on November 3, 2014
And now, looking at my list, I see that I miscounted (Oh, for Pete's sake, Debet, honestly). There are 7 candidates.
I can vote for 3 in my home district and 2 in the other, which aligns with the 5 votes I would place for option 2. The two I really like are in different districts.
posted by DebetEsse at 8:22 PM on November 3, 2014
If you only like 2 candidates, vote for them only, and do not give any votes to others, who may defeat them thereby. Of course, your one vote is unlikely to lift any of the disliked or neutral candidates above your 2 preferred ones, but that's the optimal strategy for you. (A vote for a less-preferred candidate is indistinguishable from one for your favorites, in the count.)
On preview, wha?
posted by lathrop at 8:23 PM on November 3, 2014
On preview, wha?
posted by lathrop at 8:23 PM on November 3, 2014
I guess I should add that I think it also depends on whether your strategy is to try to keep the candidates you dislike out, or make sure the candidates you like get elected. If this is a simple 'whoever has the top N votes' race, then lanthrop is right if you prefer the latter outcome. If this is a system where you can rank your preference in order, then go ahead and vote for all 5; it shouldn't matter either way.
posted by Aleyn at 8:28 PM on November 3, 2014
posted by Aleyn at 8:28 PM on November 3, 2014
This sounds close enough to approval voting that if you're trying to optimize either your understanding or the likely small utility of your personal votes, a read about hazards and strategies might be helpful.
posted by weston at 8:56 PM on November 3, 2014
posted by weston at 8:56 PM on November 3, 2014
Response by poster: lathrop, this is probably more information that you need or want, but what the heck.
I'm going to use candy to explain. I think it will help.
There are 2 groups of candidates.
Group A: Reese's, M&Ms, Hershey, and Whoppers
Group B: Skittles, Dumdums, and Necco Wafers
I can vote for up to 3 of Group A and 2 of group B. 2 from each group will take office, along with the remaining candidate with the most votes. 2 will not take office.
I really like Reese's and Skittles. I hate Whoppers and Necco Wafers. The others are fine.
I hope that helps clarify.
posted by DebetEsse at 9:02 PM on November 3, 2014
I'm going to use candy to explain. I think it will help.
There are 2 groups of candidates.
Group A: Reese's, M&Ms, Hershey, and Whoppers
Group B: Skittles, Dumdums, and Necco Wafers
I can vote for up to 3 of Group A and 2 of group B. 2 from each group will take office, along with the remaining candidate with the most votes. 2 will not take office.
I really like Reese's and Skittles. I hate Whoppers and Necco Wafers. The others are fine.
I hope that helps clarify.
posted by DebetEsse at 9:02 PM on November 3, 2014
You should vote for the person you want to win the most.
posted by Ironmouth at 9:15 PM on November 3, 2014
posted by Ironmouth at 9:15 PM on November 3, 2014
Do the Bully vote. Only vote for the two you want to win. Otherwise you risk giving the winning vote, or the vote that keeps your two out, to someone you don't like or are meh about.
posted by 724A at 9:52 PM on November 3, 2014
posted by 724A at 9:52 PM on November 3, 2014
I think voting against is a fair strategy. I would vote for the candidates who are most likely to defeat the 2 candidates you don't like. But this depends on how they are polling.
The actual value of your vote depends, as said by Jairus above, on the manner in which they keep score and there is no use voting for a candidate who will likely lose nor is there value in voting for a candidate who is sure to win.
posted by vapidave at 10:06 PM on November 3, 2014
The actual value of your vote depends, as said by Jairus above, on the manner in which they keep score and there is no use voting for a candidate who will likely lose nor is there value in voting for a candidate who is sure to win.
posted by vapidave at 10:06 PM on November 3, 2014
as Aleyn said, you need to decide whether your goal is to get your 2 preferred candidates in, or keep your 2 hated candidates out.
which of these 2 non-optimal scenarios would you prefer?
if M&Ms, Hershey, and Dumdums, then vote for the 5 you don't actively dislike (you mainly want to keep out Whoppers and Necco Wafers, even if that means neither of your 2 preferred candidates wins).
if Reese's, Skittles, and Whoppers, then vote for the 2 you actively prefer (you mainly want Reese's and Skittles to be elected, even if that means one of your hated candidates also wins).
posted by russm at 10:20 PM on November 3, 2014 [2 favorites]
which of these 2 non-optimal scenarios would you prefer?
if M&Ms, Hershey, and Dumdums, then vote for the 5 you don't actively dislike (you mainly want to keep out Whoppers and Necco Wafers, even if that means neither of your 2 preferred candidates wins).
if Reese's, Skittles, and Whoppers, then vote for the 2 you actively prefer (you mainly want Reese's and Skittles to be elected, even if that means one of your hated candidates also wins).
posted by russm at 10:20 PM on November 3, 2014 [2 favorites]
Okay, I still don't quite get how the districting and the at-large seat works. Can the at-large seat go to any one of the seven, or is it constrained to the four running in your district?
posted by gingerest at 11:14 PM on November 3, 2014
posted by gingerest at 11:14 PM on November 3, 2014
This is a very confusing system! Basically, if you have no idea of polling, you just need to weigh up what you care about more.
If you want those two in, just vote for them. That's the best you can do.
If you don't want the other two, vote for everyone else, thats the best you can do, but there's a chance you will exclude the one's you like from power.
I think this is an either or scenario, although on reflection I think the latter is a bit better. Scenario one is the best way to get the people you like elected, but in scenario two you are helping the two you like against the two you dislike, so if there are people with similar political opinions to you, that might well be enough.
posted by Cannon Fodder at 12:09 AM on November 4, 2014
If you want those two in, just vote for them. That's the best you can do.
If you don't want the other two, vote for everyone else, thats the best you can do, but there's a chance you will exclude the one's you like from power.
I think this is an either or scenario, although on reflection I think the latter is a bit better. Scenario one is the best way to get the people you like elected, but in scenario two you are helping the two you like against the two you dislike, so if there are people with similar political opinions to you, that might well be enough.
posted by Cannon Fodder at 12:09 AM on November 4, 2014
You're still not giving enough information for anyone to be able to answer this mathematically. I doubt I'm the person who can do that, but to get an answer to this properly at the very least you'd need to quantify how much you like / dislike each candidate (i.e give each a value from -100 to 100 or something). Additionally, you need to know or assume some sort of probability distribution, whether this is from poll data or just a guess. In the simplest case, by assuming that all candidates are equally likely, then as other posters have answered it would loosely come down to whether you liked the candidates you like more or less than you hate the candidates you hate. In general, you can work out what your best outcome will be by thinking about this expression:
My outcome = (probability candidate 1 gets in) x (amount I like candidate 1) + (probability candidate 2 gets in) x (amount I like candidate 2) ...
In this expression you have to judge how your vote affects the probability that each candidate gets in, and evaluate your outcome for each voting arrangement. That's quite a difficult problem as I imagine voting or not voting for one candidate affects the probabilities that other candidates get elected unequally (i.e. if two candidates are democrats, by voting for one, you'll make it proportionally more unlikely that the other won't get in, as opposed to a republican, since you're splitting a vote - I think).
The conclusion of this ramble is going to be fairly unproductive, but here goes: all I've managed to do in the last few paragraphs is convince myself that electoral analysis is hard, and there aren't easy short-cuts (at least, not that are obvious to me after half an hour). So, that leaves you with two options, one is to do it properly, by making a computer simulation of the election with poll data etc, which sounds like a lot of hassle, or the other is to go for the simplified case that other posters have suggested: decide whether you want your two favourite candidates to get in, or the two you hate to stay out.
posted by Ned G at 2:56 AM on November 4, 2014
My outcome = (probability candidate 1 gets in) x (amount I like candidate 1) + (probability candidate 2 gets in) x (amount I like candidate 2) ...
In this expression you have to judge how your vote affects the probability that each candidate gets in, and evaluate your outcome for each voting arrangement. That's quite a difficult problem as I imagine voting or not voting for one candidate affects the probabilities that other candidates get elected unequally (i.e. if two candidates are democrats, by voting for one, you'll make it proportionally more unlikely that the other won't get in, as opposed to a republican, since you're splitting a vote - I think).
The conclusion of this ramble is going to be fairly unproductive, but here goes: all I've managed to do in the last few paragraphs is convince myself that electoral analysis is hard, and there aren't easy short-cuts (at least, not that are obvious to me after half an hour). So, that leaves you with two options, one is to do it properly, by making a computer simulation of the election with poll data etc, which sounds like a lot of hassle, or the other is to go for the simplified case that other posters have suggested: decide whether you want your two favourite candidates to get in, or the two you hate to stay out.
posted by Ned G at 2:56 AM on November 4, 2014
Candy is too much typing for me, so A, B are ones you really like, L, M, N are meh, and X, Y you dislike.
There are five winners and only two candidates that you don't like, so that means at minimum three of the people you are OK with will be elected (discounting, idk, meteor strike and write-in votes). So you should typically vote for at least three people, but you have to be careful of which three. Always A and B, but only L, M, or N if they are unlikely to knock out A or B.
Let's consider some simplified scenarios, with one district:
Special case: X and Y are so popular they are sure to win, A, B, L, M, and N are all roughly tied. This is the case where you should vote for X and Y only.
X and Y are so popular they are sure to win, N is also very popular, A, B, L, and M are about tied. In this case, you should vote for A, B, and N.
A and B are so popular they are sure to win, everyone else is about tied. In this case, you should vote for A, B, L, M, and N.
Now what happens with two districts (we know that A and B are in different districts, it's extremely relevant if X and Y are also in different districts)... Still simplified...
Dist 1: A, L, M, X; Dist 2: B, N, Y...
Consider that the voting goes like this, where people to the left got more votes...
Etc. If X and Y are in the same district, it becomes completely different again. If the margins are tight or wide, completely different.
I've got to run to work, but if you can get some data about who's in which district and roughly how popular they are, you can probably work it out. Just draw a few pictures... (I used to tutor math.)
posted by anaelith at 4:50 AM on November 4, 2014 [1 favorite]
There are five winners and only two candidates that you don't like, so that means at minimum three of the people you are OK with will be elected (discounting, idk, meteor strike and write-in votes). So you should typically vote for at least three people, but you have to be careful of which three. Always A and B, but only L, M, or N if they are unlikely to knock out A or B.
Let's consider some simplified scenarios, with one district:
Special case: X and Y are so popular they are sure to win, A, B, L, M, and N are all roughly tied. This is the case where you should vote for X and Y only.
X and Y are so popular they are sure to win, N is also very popular, A, B, L, and M are about tied. In this case, you should vote for A, B, and N.
A and B are so popular they are sure to win, everyone else is about tied. In this case, you should vote for A, B, L, M, and N.
Now what happens with two districts (we know that A and B are in different districts, it's extremely relevant if X and Y are also in different districts)... Still simplified...
Dist 1: A, L, M, X; Dist 2: B, N, Y...
Consider that the voting goes like this, where people to the left got more votes...
A L M X B N YVote for A, B, and any of L, N, M.
X L M A Y N BVote for A, B, and L.
L
X M
A
N
Y B
Vote for A and B only.
L
X M A
Y N B
Vote for A and B only.
A L M X B N YVote for A, B, L, M, and N if you value keeping X and Y out the most, vote for A and B only if you value getting them in the most.
Etc. If X and Y are in the same district, it becomes completely different again. If the margins are tight or wide, completely different.
I've got to run to work, but if you can get some data about who's in which district and roughly how popular they are, you can probably work it out. Just draw a few pictures... (I used to tutor math.)
posted by anaelith at 4:50 AM on November 4, 2014 [1 favorite]
This thread is closed to new comments.
posted by Jairus at 8:16 PM on November 3, 2014 [1 favorite]