Questions tagged [voting-theory]
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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Can someone inductively prove this recursion formula? [duplicate]
This is admittedly directly related to this other question but it's a little different.
Let:
$$ a_n = \Big\lfloor (e-1)n! \Big\rfloor - 1 \qquad n \in \mathbb{Z} > 1 $$
where $e \approx$ 2....
3
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Maximising the difference between the ordering of pairs of elements in a collection of totally ordered sets
Suppose I have $M$ totally ordered sets, all of length $N$, who all share the same elements. For example, for $M=3$ and $N=4$, we can have $S_1 = \{A < B < C < D\}$, $S_2 = \{B < A < C &...
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Finding weights for the Borda count to elect any given candidate
Suppose three candidates A, B, and C run for office and voters submit their preference orders. The typical Borda count awards 2 points for a first-place vote, 1 point for a second-place vote, and 0 ...
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Pivotal's definition on arrow's impossible theorem
I'm trying to understand Arrow's impossible theorem, and I understand the idea of using extremal lemma. The pivotal is defined as the first individual who change his preference of from ranking $b$ to ...
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Probability that a uniform random variable + a constant be greater than another uniform random variable
I am trying to understand a model of probabilistic voting from the following paper https://ideas.repec.org/a/eee/pubeco/v96y2012i1p10-19.html and the one component I struggle with goes as follows:
ΔU ...
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Which Property Did the Sport Climbing Point System Violate?
In the 2020 Summer Olympics Sport Climbing was added as a new Olympic Sport.
Competitors had to compete in three categories: lead climbing, bouldering and speed climbing.
Within each category the ...
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Eigenvector of a matrix in which values normalise after multiplication
Definition:
Suppose $x\in\mathbb R$.
Then define $||x||$ the collapsing of $x$ by $||x||=0$ if $x<1$, and $||x||=1$ if $x\geq 1$.
Definition:
Suppose that
$M$ is a matrix over the closed interval $...
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Given a social system in which people are supporters of either a $G$- or a $H$-orientation, calculate the probability to have a $G$-person elected.
In this paper, Majority rule, hierarchical structures, and democratic totalitarianism: A statistical approach, I read:
A social system is considered in which people are supporters of either a $G$-...
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Best voting system where there are few voters and seferal candidates?
I'm looking at a scenario where there are few voters (2-3), and several to many candidates (20-30) where at most there is room for 3 winners.
Approval voting seems like the way to go to avoid tactical ...
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On the Condorcet Paradox
The OEIS sequence A277935 gives the number of ways 2n-1 people can vote on three candidates such that the Condorcet paradox arises. Is there a general formula for the number of ways $n$ people can ...
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Truthful budget partitioning
Suppose there is a budget $M$ that needs to be partitioned into two projects $A$ and $B$. There are two players, where the first player prefers to allocate $pM$ to A and $(1-p)M$ to $B$ (i.e., it ...
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Median Voter Models in Two Dimensions (computing area of a bounded sector)
I've been trying to work out a way of computing area for a two-dimensional median voter model I've been working on. A, B, and C are political parties that can choose where they want to be on the ...
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What properties of a voting method is best for deciding what movie to watch among a small group of people? [closed]
Almost every night me and my friends get together to watch a movie.
Current Method:
Each person (<10) picks 5 movies they want to watch and we vote on them. Each person gets around 7 votes which ...
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Game theory - three voters for two candidates nash equilibrium
There are 3 voters (x, y, and z) and two candidates (Alice and Bob). For either Alice or Bob to win they need 2 votes. If Alice wins x gets 1, y and z get 0. If Bob wins, x gets 0 and y and z get 1 ...
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Approximative formula for normal distribution being above threshold
Suppose that $X \sim \mathcal{N}(r + \frac{1}{N}, s) $ and $Y \sim \mathcal{N}(r, s)$ for some $r, s \approx 1$ and $N \approx 10^6$.
What are good approximate formulas for the quantity
$$\frac{ \...
