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
165 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
161 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
213 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
127 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
116 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 ...
7
votes
0answers
64 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 ...
5
votes
1answer
1k 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 ...
5
votes
1answer
93 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, ...
4
votes
1answer
57 views

Analyse the US presidential election from the perspective of Arrow's theory

I want to consider the voting system against the 4 Arrow's axioms. So first the voting system simplifies to first-past-the post system where the highest polling candidate wins the election. How does ...
4
votes
2answers
144 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
2answers
177 views

Number of elements in cartesian power with a majority constraint

Problem: I would like to know the number of elements in the cartesian power $X^n$ (cartesian product of one set $X$ by itself, $n$ times) with a majority constraint: how many elements in $X^n$ have a ...
4
votes
1answer
283 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
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 ...
3
votes
4answers
280 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
111 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
92 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
1answer
66 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
0answers
85 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
747 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
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 ...
2
votes
1answer
111 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
83 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
3answers
101 views

How do I weight votes based on number of possible voters?

Scenario: I have a book club that reads a book every month. My website allows the readers to give a 5 star rating to each book. We have 10 members and a rule that a member may only vote on a book they ...
2
votes
2answers
111 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
1answer
20 views

name of a fairness criterion

I found the following fairness criterion in the exercises of Excursions in Modern Mathematics: If a majority of the voters have candidate X ranked last, then candidate X should not be a winner of the ...
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
82 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
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 ...
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
2answers
83 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 ...
1
vote
1answer
216 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
80 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
660 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
54 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
47 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
633 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

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
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} = ...
1
vote
1answer
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 ...
1
vote
1answer
121 views

Reweighted Range Voting

I'm trying to create a voting system that implements RRV, yet I'm unable to fully understand the explanation from an example that I found at rangevoting.org. I'm struggling to understand the following ...
1
vote
2answers
38 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 ...
0
votes
1answer
52 views

What is the strategy-proofness of maximal lottery?

The maximal lottery system is a voting system based in game theory. It is based in game theory. The general idea is that it is better than all the other voting systems. My question is, is it ...
0
votes
1answer
88 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
49 views

Understanding the proof of Gibbard-Satterthwaite theorem

Let $n$ be the number of voters and $A$ be the set of alternatives. For voter $i$, we denote by $a \succ_i b$, if $i$ prefers $a$ to $b$, where $a,b \in A$. Let $L(A)$ denote the set of all strict ...
0
votes
1answer
40 views

How to find a quota which makes a voter a dummy voter?

I have four voters: $A$, $B$, $C$, and $D$. \begin{align*} &A\ \text{has}\ 6\ \text{votes}\\ &B\ \text{has}\ 6\ \text{votes}\\ &C\ \text{has}\ 2\ \text{votes}\\ &D\ \text{has}\ 1\ ...
0
votes
1answer
33 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
134 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
1answer
21 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 ...
0
votes
0answers
22 views

Advantages/disadvantages of a utiliarian social welfare function

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 ...
0
votes
0answers
8 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 ...