Bivariate Issues in Fair Leader Election Open Access
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All prior work in leader election algorithms deals with univariate facets. We consider multivariate issues in a broad class of fair leader election algorithms. We investigate the joint distribution of the duration of two competing candidates. Under rather mild conditions on the splitting protocol, we prove the convergence of the joint distribution of the duration of any two contestants to a limit via convergence of distance (to 0) in a metric space on distributions. We then show that the limiting distribution is a Marshall-Olkin bivariate geometric distribution. Under the classic binomial splitting we are able to say a few more precise words about the exact joint distribution and exact covariance, and to explore (via Rice's integral method) the oscillatory behavior of the diminishing covariance.