4 results for Wilson, Mark, Report, 2007

  • Random and Exhaustive Generation of Permuations and Cycles

    Wilson, Mark (2007)

    Report
    The University of Auckland Library

    In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.

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  • Asymptotics of Diagonal Coefficients of Multivariate Generating Functions

    Raichev, A; Wilson, Mark (2007-05)

    Report
    The University of Auckland Library

    This article presents some recent progress in the asymptotics of diagonal coefficients of multivariate generating functions and can be seen as an extension of [RW].

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  • Asymptotics of the Minimum Manipulating Coalition Size for Positional Voting Rules under IC Behaviour

    Pritchard, G; Wilson, Mark (2007-02)

    Report
    The University of Auckland Library

    In 1973–75 Gibbard and Satterthwaite published a fundamental impossibility theorem which states that every non-dictatorial social choice function, whose range contains at least three alternatives, at certain profiles can be manipulated by a single individual voter [6, 15]. After that, the natural question arose: if there are no perfect rules, which ones are the best, i.e. least manipulable? To this question there can be no absolute answer – it depends both on the behaviour of the voters, and on the measure used to quantify the term “manipulability”. Among models of voter behaviour, the following two have gained the most attention ([3,14]). The Impartial Culture (IC) model assumes that voters are independent, and that each voter is equally likely to vote for any candidate. The Impartial Anonymous Culture (IAC) model assumes some degree of dependency. This paper concerns itself with the IC model.

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  • A New Method for Computing Asymptotics of Diagonal Coefficients of Multivariate Generating Functions

    Raichev, A; Wilson, Mark (2007-01)

    Report
    The University of Auckland Library

    [no abstract available]

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