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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13
votes
1answer
143 views

How low can the approval rating of a majority candidate be?

“Ostrogorski's paradox” describes a strange situation in which voters decide on candidates based on issues in platforms, but on each issue of the platform, the majority of voters disapprove of the ...
8
votes
1answer
147 views

Feedback loop in real-time voting of TV show?

Today, a German TV casting show ("Unser Star Fur Baku") introduced a new "real-time" voting system that works as follows: 10 contestants take part in a song competition. Viewers can call in and vote ...
8
votes
2answers
171 views

Is there a voting method with a sane strategy?

Is there a voting method where the best strategy for strategic voters can be explained in a sane way? According to Gibbard–Satterthwaite, there is no "strategy-free" (and reasonable) voting ...
7
votes
4answers
103 views

Electoral college

"Recall that" [if one can pardon that expression] the Constitution of the United States provides that (1) the president is elected by a college of electors, and that (2) there are as many of those ...
7
votes
1answer
105 views

Does it make sense to run Meek STV with more choices than seats?

During the current batch of moderator elections at Gaming, it has been argued that since only 2 seats are up for grabs in this round of elections, it only makes sense to cast ballots by only ranking ...
4
votes
2answers
112 views

Does Arrow's Theorem apply when choosing a single best candidate?

According to Wiki, Arrow's Impossibility Theorem proves that we cannot create a social welfare function that obeys unanimity, non-dictatorship, and IIA. However, in real elections, we want to choose ...
4
votes
1answer
606 views

Gibbard–Satterthwaite Theorem versus Arrow Theorem

Arrow Theorem is a very classical result in social choice theory, stating very roughly that any reasonable voting procedure is either dictatorial or subject to tactical voting. More precisely, there ...
4
votes
1answer
95 views

Violation of the irrelevant alternative criterion of fairness in a pairwise comparison

I am teaching my students about the fairness criteria for voting system, working up towards arrow's impossibility theorem. One of the voting methods is called the pairwise comparison method: voters ...
4
votes
2answers
64 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 ...
3
votes
4answers
143 views

Question on the Condorcet Ranking (Schulze Method) Algorithm

I've been doing some research on ranking algorithms, and I've read theresearch with interest. The aspects of the Schulze Algorithm that appeals to me is that respondents do not have to rank all ...
3
votes
2answers
102 views

Locating Math Book

I am seeking the title of a math book I read several years ago and found interesting. It was intended for a general public audience and covered topics from Arrow's Voting Theorem, Hilbert's Hotel ...
3
votes
1answer
65 views

Introductory text on voting theory

Some years ago I read about a famous theorem by K. Arrow on rank-order voting systems. My interest in voting theory topic has been spurred by the use of MeekSTV in our moderator elections. As such, ...
3
votes
1answer
78 views

Stability under supremum of sets of social choice function with single peaked preferences

Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455. The setting is as follows: A non-empty finite set of ...
3
votes
0answers
39 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 ...
3
votes
1answer
272 views

Game Theory Voting

I am having some difficulty in solving the following problem. I was wondering whether someone would be kind enough to sketch a solution or even better to solve the whole game. Thanks Suppose that ...
3
votes
1answer
68 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
46 views

Anyone know about definition of weak dictator?

I am trying to prove arrow's impossibility theorem in case which ties are allowed in individual preference lists and so is social preference list. It says that if $p$ is a weak dictator, then we can ...
2
votes
1answer
75 views

Counting in Arrow's theorem

I seem to be really confused with the counting system in Arrow's theorem. Can I have a simple explanation how they determine the outcome? I can't determine the outcome using rules from my notes. It ...
2
votes
2answers
102 views

Why not n=2 in Arrow's theorem

Why in the statement of Arrow's impossibility theorem we omit the case n=2? I will appreciate it if you can explain it in easy words. I'm by no means an expert in the area (I think it's very much ...
2
votes
0answers
67 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
1answer
133 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
57 views

Which voting method is the most fair? [closed]

I have heard of Plurality Borda Count Instant Runoff Sequential Pairwise voting methods, where it mathematically can be proved which is the most fair and in which situations. From my ...
1
vote
2answers
39 views

Calculate the Ranks of Candidates based on Votes and Total Candidates

What is the formula to calculate the rank of each candidate when I have the total candidates and votes secured by each? I've managed the percentage part, but calculating the rank has me stuck. Id be ...
1
vote
2answers
497 views

Mathematical Analysis of the Electoral College

Let us consider the electoral college voting system used to elect the American president. I have a few questions from the point of view of decision-making/gaming theory. My ultimate goal is to vote in ...
1
vote
1answer
45 views

Condorcet winner and pluralism by 51%

Is it possible for the winner by pluralism to not be the Condorcer winner, if the winner by pluralism wins by 51%? This assumes 3 or more candidates. Also this assumes a rank and or preferential ...
1
vote
1answer
36 views

Are the following two definitions of Borda winner equivalent?

The Borda count is a method used to determine the winner object where people rank objects. For instance, imagine each person ranking 3 objects. The highest ranked object gets 2 points, the second gets ...
1
vote
2answers
188 views

What is the difference between social choice function and social welfare function?

I am trying to understand a shard proof on Arrow's Impossibility Theorem and Gibbard-Satterthwaite Theorem. I stumbled upon these 2 different functions, and I cannot understand the difference between ...
1
vote
1answer
30 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 ...
1
vote
0answers
57 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 ...
0
votes
2answers
77 views

Decide the most favorable candidate

Consider an election voting process where people need to elect a representative among n number of candidates. Is there an approach to determine the most favorable option? Voting just a single person ...
0
votes
1answer
77 views

Getting as close to a target vector as possible

Say I have P number of political parties in an election that I'm trying to rig. My boss has decided what number of percentage of the votes it is best that each party should get. N number of votes have ...
0
votes
1answer
29 views

Can any information be gathered from the list of people who did or did not vote

I have found out to my surprise that the list of who did or did not vote is publically available in Texas. My question is, can information regarding my preference be ascertained by the fact that I ...
0
votes
3answers
129 views

Fair selection of most popular items among separate voting sets

This is a practical problem that arose in real life, which I believe creates interesting mathematical questions. There is a festival of small plays lasting 8 weeks. Each week 10 short plays are ...
0
votes
0answers
18 views

Questions about arrow's impossibility theorem.

If we had chosen to work in a context where ties are allowed in the individual preference lists, then Arrow’s Theorem no longer holds with the conclusion that there is a person whose list is always ...
0
votes
0answers
16 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 ...
0
votes
0answers
17 views

Is there a yes or no voting system where no losing coalitions exist?

I am just wondering. It may sound silly, but Is it possible for yes or no voting system to have only winning coalitions? Basically, any set of voters is winning and only empty set, in which nobody ...
0
votes
0answers
15 views

Can anyone find a quota for this question?

I have 4 voters A has 6 votes B has 6 votes C has 2 votes D has 1 vote And I have to find out a quota such that D in only a dummy voter, which is adding it to losing coalition still makes it ...
0
votes
0answers
23 views

does anyone know about “hare system” ?

I am studying mathematical modeling in political science. There is a voting procedure called "Coombs system", which is opposite to hare system. You are eliminating the least first place votes and by ...
0
votes
1answer
52 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
31 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 ...