# What is a good voting system that is based on a value and number/frequency of votes?

So let's suppose there are n candidates running for office. A bunch of random people begin to selectively vote the candidates, each vote being a number from 1 to n. What is a good way to order the candidates based on their vote number and also the number of votes/frequency of votes?

So for example: If candidate A was voted by a bunch of voters, but was the votes were fairly spaced out, he would probably be considered "not as great" as a candidate who was voted less/same amount/more but the votes were shortly after one another.

I was thinking of something like Reddit's Karma system, but that only takes into accounts +1's and -1's (and I'm not even sure if Reddit every gave information on how their Karma system works!)

So for example:

Candidates = [ Bob, Sally, Joe, Sam, Rob]

Person A ranks Sally as #1 (best choice) and [Bob, Rob] as #5 (worst choice) and leaves (he doesn't vote for others).

Person B ranks Sam as #2, Joe as #4, and leaves.

Person C ranks Sally as #1, Joe as #3, and Bob as #5.

So in this case it may be compelling to say Sally is close to being #1, while Bob is probably closer to being #4 or #5. But Sam was only voted once as #2 and as such there's not a whole lot of grounds to say "yes he's definitely #2". Similarly, Rob was only voted once as being #5 but there isn't sufficient votes to definitively say he's worse than Bob.

As such, the raking may become something like:

Sally > Sam > Joe > Rob > Bob

You can probably twist this example to have even more voters and create a few outliar, but I hope his gives you a general idea of what I'm looking for.

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Is there a particular reason why bunched together votes are more worthwhile? Do you care how recent the votes are? Also when you say random people selectively vote the candidates, do they vote for a single candidate, or for multiple, and are they ranked or scored in some fashion? Noted ranked preference systems are the Condorcet method and instant run-off voting. –  tristan Aug 22 '12 at 9:28
Well if it's more recent it means that people aren't 'hesitating' to vote for him. The votes shouldn't be more than a week apart. They vote for multiple candidates and are voting them from 1 to n. –  Apothem Aug 22 '12 at 15:03
Does each voter rank every candidate relative to the other candidates, and you want to produce an overall ranking? Or do voters just vote for some candidates and you want a single winner? If the former, you might read about Arrow's voting paradox –  Henry Aug 22 '12 at 22:01
An overall ranking is what I'm looking for; it's something to see "candidate a is better than candidate b is better than candidate c" and so on. –  Apothem Aug 23 '12 at 6:14
I did read the summary of Arrow's voting paradox, but I'm hoping that for what I'm working on a group of people who vote will have some amount of common grounds. So in reality it's a subset of a group 1...N who are each of the same "class" votes for their own group. Then another subset of group N+1...M who are each of the same "class" votes for their own group as well. And so on. I hope that makes sense... –  Apothem Aug 23 '12 at 6:25