Two Multinomial Random Sociometric Voting Models

Abstract

Two multinomial random sociometric voting models are presented to study the critical number of votes that can occur under peer voting schemes. Assumed in Model I are equal probabilities of votes for each candidate other than self. The given conditions are that a fixed number of ballots are cast (denoted by N) and there are exactly b-N abstentions (N ≤ b). Model I incorporates the restriction of not voting for self; Model II is presented without this restriction. Abstentions are possible under both models. Empirical evidence for the convergence of the two models is presented so that Model II can be substituted for Model I in groups where b ≥ 8 regardless of the value of N (ballots cast). This substitution greatly simplifies calculation of the critical values (r) of sociometric frequencies attributed in classroom groups which vary in size. Appendices present tables for Models I and II for various values of r when b and N are less than or equal to 8. A table is also given for Model II up to N=b=50.