Help with a semi-mathematical solution?

[Gaelrond]

Ok, trying to figure out the best way to do a small election, all methods tried in the past seem overly complex, so I'm looking for some ideas. Keep in mind this is a very small organization, with around 2 dozen total members; resources are not unlimited. Generally elections are done around a large table, with small pieces of paper folded and collected in a hat before being counted. Here are the other stipulations:

-The ballots are secret
-There is a possible maximum of around 24 voters, typically the number is 15-17 in attendance on election night.
-There will be anywhere between 3 and 9 or so candidates for 3 total positions.

I think that's about it... Methods tried in the past:

-Each voter votes for 3 candidates on a single ballot sheet, top three vote-getters are elected.
-Three consecutive votes, each voter votes for a single candidate in each vote. Again, top three vote-getters are elected. As candidates are elected, their names are removed from the list of candidates.
-One vote taken, each voter votes for a single candidate. Top three vote-getters are elected.

Can't think of anything else, but am hoping for some thoughtful input towards an easier/more efficient way to elect people.

Thanks!

[leng]

Arrgh. You are stumbling into a minefield if you go too deeply here. PhD theses have been written on the fairness of various voting schemes and their vulnerability to tactical voting. Mind, with a constituency of 24 most of the statistics become dubious.

The voting method I am most familiar with in these circumstances is called Single Transferrable Vote which is designed to allow (almost) every vote to have some influence on the outcome. STV counting can get quite complex (see this Wikipedea article (http://en.wikipedia.org/wiki/Single_Transferable_Vote) to get a flavour of the issues).

To try something simple which is not too difficult to count, you could use a very rudimentary transferrable vote system.

1.Each voter ranks as many candidates as he is happy with in preference order.
2.Pile the votes according to first preference.
3.Redistribute the smallest pile according to second preference, eliminating that candidate.
4.Repeat 3, taking the first non-eliminated candidate as the preference for that voter, until there are only 3 candidates left.

The problem here is what you do with low-vote draws when you have such a small electorate. Also, this method has the inherent flaw that it is technically possible for the second-most unpopular first choice to get elected by the transfers (the least-hated candidate syndrome).

Personally, I'd go for your first method on the basis of simplicity and convenience.

Alternatively, try a dutch auction. Each candidate puts an amount of money in the pot (not declared to the other candidates). The three highest contributors are elected and all the money in the pot is distributed to the non-candidate voters. This closely models a modern democratic system (except for the bit about redistributing the money).

[Lycos]

Let's make a poll! :D

I think the previous methods are all rather logical. I don't see many other options other than what leng mentioned and the previous methods.

[DirkDarkBlade]

We have a similar situation except our group is 120 folks.

We give each person a sheet of paper with three blanks. The voter puts the name of three candidates on the paper (the three they want to win the election).

We collect the papers and tally the votes. The three people with the most votes are elected.

Mind you until recent years most elections have only had three candidates so the voting/counting was easy.

Thats how we do it.

[Raveneye]

Uh, 47

[Shiz]

Give everyone 24 (or how many voters show up) X 3 (spots to fill) votes. People can cast all or some for each candidate. The three candidates with the most "votes" win. This is the cumulative voting model from shareholder elections. It lets someone make a big impact for the person they REALLY want to win.

Not sure how this would work but it would be fun to try!

[leng]

Give everyone 24 (or how many voters show up) X 3 (spots to fill) votes. People can cast all or some for each candidate. The three candidates with the most "votes" win. This is the cumulative voting model from shareholder elections. It lets someone make a big impact for the person they REALLY want to win.

Not sure how this would work but it would be fun to try!
This is known as the "Eurovision Song Contest" election model. Each elector has a pool of votes that they can distribute across the list as they wish (except they cannot vote for themselves)

[Gaelrond]

Well... the three positions aren't the only ones that wind up being voted for, but those are the only ones that are causing difficulty, since the three positions are of equal rank.

It's not so much that the method currently used doesn't work, it just strikes me as painfully inefficient. I'm just looking for a way to streamline it; it may not really be possible. Plus each method seems to have some flaws... for example if you just go with the top 3 vote getters overall, the winner might get 15 votes, while the next two might each only get 1 or 2. Not sure I want to have someone elected who only gets 2 votes...

Anyways... it's not really broken, I just wanted to see if I could improve it. Thanks for the input, I'll keep thinking...

[Sylvene]

To prevent the scenario you just listed and to have as few little admin work as possible, then method 1 should be employed. 1 vote, 3 names. You have to vote for 3 different people. Top 3 vote getters get in.

[Gaelrond]

To prevent the scenario you just listed and to have as few little admin work as possible, then method 1 should be employed. 1 vote, 3 names. You have to vote for 3 different people. Top 3 vote getters get in.

The only potential problem I can see with that method is if there are, say 7 candidates for the 3 positions, even with the full membership present and voting, the top 3 might only get 4-5 votes each. It's a bit of a conundrum- the method has to be as fair as possible, but ideally it will prevent an unpopular candidate from being elected (I mean, 5 votes out of 20% is hardly popular, IMO) as well.

My dad and I were discussing it the other night, and we agreed that perhaps elections are not the way to go about it. The elections are for the Board of Officers for the Webster Special Police, of which my father is a member, and I am a probational (and thus non-voting) member. My dad's thought was to basically eliminate nominations by listing every member eligible for a position, then remove any who do not wish to be considered. That establishes your pool of candidates, from which you vote. What he'd rather see, and I tend to agree, is to have the officers appointed by the Governing body under whose authority we fall. In this case I believe that would be the town board. At the very least, have the Chief appointed by the Town Board, and then the Chief has the authority to appoint officers as he sees fit. The Officers Board, as it stands now, consists of:

1 Chief
1 Lieutenant
3 Sergeants
1 Corporal

The three Sergeant positions are the ones that cause the headache during voting. Ultimately, I guess it's not that big a deal, as long as it gets done and everyone agrees that it was done fairly.

[DirkDarkBlade]

Hey now I understand. And no you don't have to have elections. They are policemen so they are armed. Put all the Sergeants together and the three strongest survivors win! (j/k)

Only thing I'd see about letting the chief appoint is you could end up with the "good ole boy" network where the Chief appoints his friends and not necessarily the best folks for the job. Its just a thought.

[Lycos]

Only thing I'd see about letting the chief appoint is you could end up with the "good ole boy" network where the Chief appoints his friends and not necessarily the best folks for the job. Its just a thought.

I completely agree. That is what you'll get all the time then. If it's a good "good ole boy" group then things will probably work out ok. It's when you get the bad "good ole boy" group that things go horribly wrong. Plus, it hampers the enthusiasm of the younger guys who will keep the organization strong. Why should they bother doing anything since they have no real chance of "making a difference" if the same "good ole boys" will be in charge year after year.