Articles containing proofs | Probability problems | Theorems in combinatorics | Probability theorems | Enumerative combinatorics
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with p > q, what is the probability that A will be strictly ahead of B throughout the count?" The answer is The result was first published by W. A. Whitworth in 1878, but is named after Joseph Louis François Bertrand who rediscovered it in 1887. In Bertrand's original paper, he sketches a proof based on a general formula for the number of favourable sequences using a recursion relation. He remarks that it seems probable that such a simple result could be proved by a more direct method. Such a proof was given by Désiré André, based on the observation that the unfavourable sequences can be divided into two equally probable cases, one of which (the case where B receives the first vote) is easily computed; he proves the equality by an explicit bijection. A variation of his method is popularly known as André's reflection method, although André did not use any reflections. The Bertrand's ballot theorem is equivalent to the Cycle lemma. (Wikipedia).
Voting Theory: Plurality Method and Condorcet Criterion
This video explains how to determine the winner of an election using the plurality methods and how to determine the Condorcet winner. Site: http://mathispower4u.com
From playlist Voting Theory
Democracy is mathematically impossible.
Determining the "will of majority" is badly defined. Why should we believe the two- round voting system if there are many other ways to quantify people's preferences ? In this video I discuss the manipulations, paradoxes and other problems associated with the mathematics of voting. My
From playlist Something you did not know...
Voting Theory: Fairness Criterion
This video define 4 Fairness Criterion for determining the winner of an election. Site: http://mathispower4u.com
From playlist Voting Theory
(New Version Available) Introduction to Voting Theory and Preference Tables
Updated Version: https://youtu.be/WdtH_8lAqQo This video introduces voting theory and explains how to make a preference table from voting ballots. Site: http://mathispower4u.com
From playlist Voting Theory
Ramsey theory is based on Ramsey's theorem, because without it, there would be no Ramsey numbers, since they are not well-defined. This is part 2 of the trilogy of the Ramsey numbers. Useful link: https://en.wikipedia.org/wiki/Ramsey%27s_theorem#2-colour_case Other than commenting on the
From playlist Ramsey trilogy
Voting Theory: Monotonicity Criterion Using Instant Runoff Voting
This video explains the Monotonicity Criterion and how it can affect the outcome of an election when using instant runoff voting. Site: http://mathispower4u.com
From playlist Voting Theory
Voting Theory: Approval Voting
This video explains how to apply the approval voting method to determine the winner of an election. Site: http://mathispower4u.com Content Source: http://www.opentextbookstore.com/mathinsociety/
From playlist Voting Theory
Xavier Viennot: Heaps and lattice paths
CIRM HYBRID EVENT Recorded during the meeting "Lattice Paths, Combinatorics and Interactions" the June 25, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Combinatorics
AN ELEMENTARY PROOF OF BERTRAND'S POSTULATE! Special #SoMe1
I love when a deep result in mathematics is provable only with elementary techniques, like basic knowledge of combinatorics and arithmetic. In this video I will present the queen of this proofs, namely the Erdős' proof of the Bertrand's postulate, which states that it is always possible to
From playlist Summer of Math Exposition Youtube Videos
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Math for Liberal Studies - Lecture 2.6.1 Arrow's Theorem
This is the first video lecture for Math for Liberal Studies Section 2.6: Impossibility and Alternative Ballots. In this lecture, I discuss Arrow's Theorem, which explains why we have had so much trouble finding a "fair" election method. We also talk about ways to use alternative ballots t
From playlist Math for Liberal Studies Lectures
Arrow's Impossibility Theorem | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi The bizarre Arrow’s Impossibility Theorem, or Arrow’s Paradox, shows a counterintuitive relationship between fair voting procedures and dictatorships. Start your free t
From playlist An Infinite Playlist
Thomas Ransford: Constructive polynomial approximation in Banach spaces of holomorphic functions
Recording during the meeting "Interpolation in Spaces of Analytic Functions" the November 21, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio
From playlist Analysis and its Applications
Not every voting system generates impossibility: Score Voting and Impossibility
Not every voting system generates impossibility in the sense of Arrow's Impossibility theorem. That is there are voting systems that have the Weak Pareto, Independence of Irrelevant Alternatives, and Non-Dictatorial properties simultaneously. In particular we look at the relationship betwe
From playlist The New CHALKboard
Journée des lycées 2022 au CIRM
From playlist OUTREACH - GRAND PUBLIC
La théorie l’information sans peine - Bourbaphy - 17/11/18
Olivier Rioul (Telecom Paris Tech) / 17.11.2018 La théorie l’information sans peine ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com
From playlist Bourbaphy - 17/11/18 - L'information
CERIAS Security: Electronic Voting: Danger and Opportunity 5/6
Clip 5/6 Speaker: Edward W. Felten · Princeton University Electronic voting machines have made our elections less reliable and less secure, but recent developments offer hope of a better system in the future. Current research offers the hope of a future voting system that is more reliabl
From playlist The CERIAS Security Seminars 2008
Math for Liberal Studies - Lecture 2.6.2 Approval and Range Voting
This is the second video lecture for Math for Liberal Studies Section 2.6: Impossibility and Alternative Ballots. In this lecture, we explore the alternative ballots discussed in the previous lecture. We learn how to find the winner of an election using this ballots, and also explore some
From playlist Math for Liberal Studies Lectures
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus