Charles Dodgson (1866) introduced a method to calculate matrices determinant, in asimple way. The method was highly attractive, however, if the sub-matrix or the mainmatrix determination is divided by zero, it would not provide the correct answer. Thispaper explains the Dodgson method's structure and provides a solution for the problemof "dividing by zero" called "virtua...

With the Dodgson rule, cloning the electorate can change the winner, which Young (1977) considers an “absurdity”. Removing this absurdity results in a new rule (Fishburn, 1977) for which we can compute the winner in polynomial time (Rothe et al., 2003), unlike the traditional Dodgson rule. We call this rule DC and introduce two new related rules (DR and D&). Dodgson did not explicitly propose t...

Bertolacini, R. J. & Barney, J. E. (1957). Analyt. Chem. 29, 281. Dodgson, K. S. & Lloyd, A. G. (1957). Biochem. J. 66, 532. Dodgson, K. S., Lloyd, A. G.& Spencer, B. (1957). Biochem. J. 65, 131. Dodgson, K. S., Rose, F. A. & Tudball, N. (1958). Biochem. J. 71, 10. Dodgson, K. S. & Spencer, B. (1953). Biochem. J. 55, 436. Dodgson, K. S. & Spencer, B. (1957). Meth. biochem. Anal. 4, 211. Dodgson...

This paper compares binary versions of two well−known preference aggregation methods designed to overcome problems occurring from voting cycles, Copeland’s (1951) and Dodgson’s (1876) method. In particular it will first be shown that the Copeland winner can occur at any position in the Dodgson ranking. Second, it will be proved that for some list of individual preferences over the set of altern...

It is known that Dodgson’s rule is computationally very demanding. Tideman (1987) suggested an approximation to it but did not investigate how often his approximation selects the Dodgson winner. We show that under the Impartial Culture assumption the probability that the Tideman winner is the Dodgson winner tend to 1. However we show that the convergence of this probability to 1 is slow. We sug...

Computing the Dodgson Score of a candidate in an election is a hard computational problem, which has been analyzed using classical and parameterized analysis. In this paper we resolve two open problems regarding the parameterized complexity of DODGSON SCORE. We show that DODGSON SCORE parameterized by the target score value k has no polynomial kernel unless the polynomial hierarchy collapses to...

In assaying for sulfatases it is possible to use several methods which have been devised for the determination of inorganic sulfate. As a test for chondrosulfatase, the micro benzidine method developed by Dodgson and Spencer (1) is usually employed. This method appears to be the most suitable because of its good sensitivity and absence of substrate interference, but its technique is complicated...