  The voting process is formalized as a multistage voting model with successive
alternative elimination. A finite number of agents vote for one of the
alternatives each round subject to their preferences. If the number of votes
given to the alternative is less than a threshold, it gets eliminated from the
game. A special subclass of repeated games that always stop after a finite
number of stages is considered. Threshold updating rule is proposed. A computer
simulation is used to illustrate two properties of these voting games.
