# Tagged Questions

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

70 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 ...
39 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 ...
75 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 ...
90 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 ...
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 ...
30 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 parts?
32 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 ...
31 views

### Counterexample to each Arrow's axiom

I am trying to find ways that combine group preferences which hold for 3 out of the 4 Arrow's axioms. Here is what I have come up with so far: Unrestricted Domain Not sure what scheme would ...
30 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 ...
28 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 ...
111 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 ...
44 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 ...
69 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 ...
95 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 ...
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 ...
82 views

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: $\mathcal{f}... 0answers 67 views ### Ranking a set – is pair-based voting a good idea? I have a set which I want to rank based on which entry people favor the most. The set consists of too many entries for the voters to sort the entire list, and since the set contains some mainstream ... 0answers 27 views ### What is a good introductory book on Rational Choice Theory for a mathematician? I'm interested in Rational Choice Theory as an approach to political science. Amongst other, related subjects, I'd like to know a thing or two about Arrow's impossibility theorem (and other aspects of ... 0answers 22 views ### Voting mechanics clarification I am reading the following paper: http://www.jstor.org/stable/10.1086/587624 and I am confused about one of the definitions at the start of section III. The auther defines$\bar{U} = \sum_{i=m}^n\...
80 views

If a planner obeys anonymity and strong Pareto principle (individual preferences carry over to the group), then the social utility function will be: $W(x)=\sum_{i=1, ..., n}U_i(x)$ i.e. summing ...
9 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 ...
33 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 ...
20 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 ...
33 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 single-...
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. ...
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 ...