For questions regarding the mathematical analysis of voting systems and behavior. Examples include the median voter theorem or the Condorcet jury theorems.

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4
votes
2answers
69 views

Fair continuous election algorithm in a limited set of users

I have an election method in mind, don't know if already exists but I think there must be. It is used in a finite set of users and continuous. Every round, somebody is picked randomly depending on ...
1
vote
2answers
36 views

IRV failing monotonicity criterion

I am looking for the simplest possible example of instant runoff voting failing the monotonicity criterion. By “simplest possible” I mean the scenario with the fewest number of candidates $(3)$ and ...
3
votes
1answer
54 views

Algorithm for assigning users to “buckets” according to users' preferences and ranking

Suppose there is a set of $n$ users which must each be assigned to one, and only one, of $k$ mutually exclusive "buckets". However, the number of users allocated to the $i$-th bucket must be no lower ...
3
votes
1answer
89 views

Photo Rating System based of Community 'Likes'

I'm hoping to get some assistance from some math gurus on a troubling problem i'm having with a website. The site has a very large gallery (millions of photos) which are uploaded by users. The users ...
2
votes
1answer
146 views

What is the general formula for electoral districts tying.

I apologize if this question is a bit of a read. (You might want to get a frosty beverage.) Professor Alan Natapoff of MIT demonstrated, if 9 Voters are districted into 3 electoral districts of 3 ...
1
vote
1answer
28 views

Boolean functions and characters

I'm trying to solve this, but I have no idea how to start! I'm not even sure what the question is really asking. Can anybody rephrase this and perhaps give me pointers/solutions for one of the ...
1
vote
1answer
31 views

How many voters can one find in a set?

Recently some german federal states had elections. The news used to say that every n-th voter chose party X. While sitting in the train I was thinking about the following. Someone counts all persons ...
0
votes
1answer
21 views

Pairwise majority voting and Arrow's axioms

The following is a question on Arrow's theorem with a pairwise majority decision. The bits I was unsure about was (bi) (is the 4th condition satisfied?) and also is (bii) correct? Thanks for your help ...
0
votes
1answer
24 views

Gaining intuition as to why maximal lotteries use randomness to break general ties

The maximal lottery is a voting system based on choosing an optimal candidate game-theoretically. If a winner isn't clear (there is no condorcet winner), then it will return probabilities as to which ...
0
votes
1answer
104 views

Find a voting system - possibly Schulze Method

I remember the Schulze Method from back when I was studying Econ... that was years ago and my math isn't the greatest, go easy on me. We are piloting a project to make a to-do list app for teams, I'm ...
0
votes
1answer
43 views

Normalizing votes based on source's rank

If article a from source A has 100 votes, and article b from source B has 10 votes, without simply saying that article a is better because it was voted more, how can I normalize the weight of these ...
7
votes
0answers
62 views

Can Continuous Time Markov Chains be used as a reasonable voting system?

I just compared a couple of example elections, as given on Wikipedia to show how Condorcet-methods differ from non-Condorcet ones, to what happens if you just interpret the underlying preference ...
3
votes
0answers
84 views

What is the math behind calling election seats with confidence, before all votes have been counted?

On election night, predictions are made on the winner of each district, after only a fraction of the vote has been counted up. How is this done? Say there is a seat up for election, and 10,000 votes ...
2
votes
0answers
33 views

How does the Borda count work?

I was watching this video. about ranking a bunch of proposals by dividing the full list in to sub lists and each person that submitted the proposals gets one of these sub-lists and ranks it. The lists ...
2
votes
0answers
81 views

Proof of two properties of a simple math function

I would like to define a function to evaluate the value for some entities which receive a number of "up"s ($\mathcal{u}$) and "down"s ($\mathcal{d}$). I devised the following function: ...
2
votes
0answers
67 views

Ranking a set – is pair-based voting a good idea?

I have a set which I want to rank based on which entry people favor the most. The set consists of too many entries for the voters to sort the entire list, and since the set contains some mainstream ...
1
vote
0answers
21 views

Voting mechanics clarification

I am reading the following paper: http://www.jstor.org/stable/10.1086/587624 and I am confused about one of the definitions at the start of section III. The auther defines $\bar{U} = ...
0
votes
0answers
7 views

Algorithm to determine popularity through sentiment, volume, time, and feedback

I am quite new to this space of ranking algorithms, and I'm faced with a problem. I have the following factors that will determine an entity's "popularity" ranking: Number of occurrences mentioned ...
0
votes
0answers
22 views

Show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms.

I want to show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms. Given at least three rewards, and at least two individuals, there is no ...
0
votes
0answers
15 views

Sen's theorem on minimal liberalism

I want to solve the following question regarding Sen's theorem and preferences orderings. The bit I am having trouble with is 2b Question 1: Describe Sen's theorem ('paradox') There is no social ...
0
votes
0answers
31 views

Voting Systems without tactical voting

Which voting systems do not have tactical voting? Specifically, expressing your true preference on a ballot will not result in a less favorably outcome. I'm looking at both multiple-winner and ...
0
votes
0answers
14 views

For which voting system are multiple parties stable?

Most voting systems gravitate to two parties over time (namely, there is a bias to two candidates receiving a disportionate amount of votes.) For which voting systems does this not occur, i.e. ...
0
votes
0answers
18 views

Formula/theory to detect the desired number of workshop topics

I need to prepare a workshop and at the end of the workshop I want participants to choose from a set of questions (e.g. n=20) only x (e.g. x=5) questions to discuss. Therefore I want to give each ...
0
votes
0answers
20 views

Optimal voting algorithm for two-person position

Say there is an election for a position filled by two people (e.g. two senators), and n people are running in the race. Considering that preferences may vary (e.g. some people might think candidates ...
0
votes
0answers
25 views

Difference between set(determined) but unknown result and not yet determined result in terms of probability

Lets say that 44 respondents vote for something, 39 againts and 17 didn't respond or didn't make a decision, yet. Does it change anything in regard to probability that the voting will pass if we know ...