scholarly journals Some distribution results on generalized ballot problems

1985 ◽  
Vol 30 (3) ◽  
pp. 157-165
Author(s):  
Jagdish Saran ◽  
Kanwar Sen
Keyword(s):  
1981 ◽  
Vol 12 (4) ◽  
pp. 613-619
Author(s):  
Jagdish Saran ◽  
Kanwar Sen
Keyword(s):  

1969 ◽  
Vol 65 (3) ◽  
pp. 755-757 ◽  
Author(s):  
C. C. Heyde

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).


1964 ◽  
Vol 1 (01) ◽  
pp. 168-172
Author(s):  
Ora Engelberg

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.


1964 ◽  
Vol 1 (1) ◽  
pp. 168-172 ◽  
Author(s):  
Ora Engelberg

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.


2006 ◽  
Vol 38 (3) ◽  
pp. 804-826
Author(s):  
Kei Kobayashi ◽  
Hideki Kawasaki ◽  
Akimichi Takemura

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.


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

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