ballots is equivalent to deciding an arbitrary "approval cutoff." All candidates preferred to the cutoff are approved, all candidates less preferred are not approved, and any candidates equal to the cutoff may be approved or not arbitrarily. Sincere strategy with ordinal preferences A sincere voter with multiple options for voting sincerely still has to choose which sincere vote to use. Voting strategy is a way to make that choice, in which case strategic approval voting includes sincere voting, rather than being an alternative to it. This differs from other voting systems that typically have a unique sincere vote for a voter. When there are three or more candidates, the winner of an approval voting election can change, depending on which sincere votes are used. In some cases, approval voting can sincerely elect any one of the candidates, including a Condorcet winner and a Condorcet loser, without the voter preferences changing. To the extent that electing a Condorcet winner and not electing a Condorcet loser is considered desirable outcomes for a voting system, approval voting can be considered vulnerable to sincere, strategic voting. In one sense, conditions where this can happen are robust and are not isolated cases. On the other hand, the variety of possible outcomes has also been portrayed as a virtue of approval voting, representing the flexibility and responsiveness of approval voting, not just to voter ordinal preferences, but cardinal utilities as well. Dichotomous preferences Approval voting avoids the issue of multiple sincere votes in special cases when voters have dichotomous preferences. For a voter with dichotomous preferences, approval voting is strategy-proof (also known as strategy-free). When all voters have dichotomous preferences and vote the sincere, strategy-proof vote, approval voting is guaranteed to elect the Condorcet winner, if one exists. However, having dichotomous preferences when there are three or more candidates is not typical. It is an unlikely situation for all voters to have dichotomous preferences when there are more than a few voters. Having dichotomous preferences means that a voter has bi-level preferences for the candidates. All of the candidates are divided into two groups such that the voter is indifferent between any two candidates in the same group and any candidate in the top-level group is preferred to any candidate in the bottom-level group. A voter that has strict preferences between three candidates—prefers A to B and B to C—does not have dichotomous preferences. Being strategy-proof