Ballot problems

1962 ◽  
Vol 1 (2) ◽  
pp. 154-158 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Ballot Problems

Some distribution results on unconditional ballot problems

1981 ◽  
Vol 12 (4) ◽  
pp. 613-619
Author(s):  
Jagdish Saran ◽  
Kanwar Sen
Keyword(s):  
Ballot Problems

A derivation of the ballot theorem from the Spitzer–Pollaczek identity

1969 ◽  
Vol 65 (3) ◽  
pp. 755-757 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Random Walk ◽  
General Theory ◽  
Special Class ◽  
Short Note ◽  
Extensive Literature ◽  
Comprehensive List ◽  
Reduction Problem ◽  
Ballot Theorem ◽  
Ballot Problems

Over a period of many years there has developed an extensive literature on ballot problems. These, in effect, constitute a very special class of random walk problems, and their recent continued development has been justified by the apparent difficulty of reducing expressions given by the general theory down to the very simple ones that it is possible to obtain in an elementary fashion. In this short note we show that the obstacle presented by this reduction problem is actually a rather small one. For background to the above comments, together with a fairly comprehensive list of references to the ballot theory and its attendant applications, the reader is referred to Takács(2).

Exact and limiting distributions of the number of lead positions in “unconditional” ballot problems

1964 ◽  
Vol 1 (01) ◽  
pp. 168-172
Author(s):  
Ora Engelberg
Keyword(s):  
Probability Distributions ◽  
Limiting Distributions ◽  
Ballot Problems

In a ballot, candidate A scores a votes and candidate B scores b votes. Suppose the ballots are drawn out one at a time, and denote αr and βr the number of votes registered for A and B, respectively, among the first r votes recorded. Further, let Δ a,b be the number of subscripts r satisfying the strict lead condition , let be the number of subscripts r satisfying the weak lead condition ; and suppose all possible () voting records are equally probable. The probability distributions of the number of strict and weak lead positions corresponding to and , respectively, have been determined in [4] for a≧b.

Exact and limiting distributions of the number of lead positions in “unconditional” ballot problems

1964 ◽  
Vol 1 (1) ◽  
pp. 168-172 ◽  
Author(s):  
Ora Engelberg
Keyword(s):  
Probability Distributions ◽  
Limiting Distributions ◽  
Ballot Problems

In a ballot, candidate A scores a votes and candidate B scores b votes. Suppose the ballots are drawn out one at a time, and denote αr and βr the number of votes registered for A and B, respectively, among the first r votes recorded. Further, let Δa,b be the number of subscripts r satisfying the strict lead condition , let be the number of subscripts r satisfying the weak lead condition ; and suppose all possible () voting records are equally probable. The probability distributions of the number of strict and weak lead positions corresponding to and , respectively, have been determined in [4] for a≧b.

scholarly journals Parallel matching for ranking all teams in a tournament

2006 ◽  
Vol 38 (3) ◽  
pp. 804-826
Author(s):  
Kei Kobayashi ◽  
Hideki Kawasaki ◽  
Akimichi Takemura
Keyword(s):  
Lattice Path ◽  
Parallel Sorting ◽  
Sorting Algorithms ◽  
Efficient Scheme ◽  
Parallel Matching ◽  
Ballot Problems ◽  
Path Counting ◽  
Lattice Path Counting

We propose a simple and efficient scheme for ranking all teams in a tournament where matches can be played simultaneously. We show that the distribution of the number of rounds of the proposed scheme can be derived using lattice path counting techniques used in ballot problems. We also discuss our method from the viewpoint of parallel sorting algorithms.

Lattice Paths with Diagonal Steps

1969 ◽  
Vol 12 (6) ◽  
pp. 847-855 ◽  
Author(s):  
E. Goodman ◽  
T.V. Narayana
Keyword(s):  
Lattice Paths ◽  
Ballot Problems

The André-Poincaré "probléme du scrutin" [9] can be stated as follows: In an election between two candidates A polls m votes, B polls n, m > n. If the votes are counted one by one what is the probability that A leads B throughout the counting? Many derivations and interpretations of the solution have been given and a convenient summary of methods till 1956 can be found in Feller [1]. So numerous are the generalizations of ballot problems and their applications since this date that we do not even attempt an enumeration here.

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