Which alternative is selected when voters are called to participate in a sequential voting? Does the ordering matter? The current approach is the first attempt to analyze these questions. Specifically, we propose a two- alternative sequential voting procedure in which two voters are randomly ordered. Each voter has complete information about the preference of both of them. The alternative is implemented if there is unanimity. We obtain that the most patient individual has some advantage in the election, but it is not enough to guarantee that his most-preferred alternative will be selected. The probability to vote first also plays a central role, since the election also depends on the voting order. Keywords: Sequential Voting; Random order; Sub-game perfect equilibrium