  We study a modification of the so-called Parrondo's paradox where a large
number of individuals choose the game they want to play by voting. We show that
it can be better for the players to vote randomly than to vote according to
their own benefit in one turn. The former yields a winning tendency while the
latter results in steady losses. An explanation of this behaviour is given by
noting that selfish voting prevents the switching between games that is
essential for the total capital to grow. Results for both finite and infinite
number of players are presented. It is shown that the extension of the model to
the history-dependent Parrondo's paradox also displays the same effect.
