not voting for a more preferred candidate if there 4 candidates or more. Other strategies are also available and coincide with the optimal strategy in special situations. For example: Vote for the candidates that have above average utility. This strategy coincides with the optimal strategy if the voter thinks that all pairwise ties are equally likely Vote for any candidate that is more preferred than the expected winner and also vote for the expected winner if the expected winner is more preferred than the expected runner-up. This strategy coincides with the optimal strategy if there are three or fewer candidates or if the pivot probability for a tie between the expected winner and expected runner-up is sufficiently large compared to the other pivot probabilities. This strategy, if used by all voters implies at equilibrium the election of the Condorcet winner whenever it exists. Vote for the most preferred candidate only. This strategy coincides with the optimal strategy when there is only one candidate with a positive prospective rating. Another strategy is to vote for the top half of the candidates, the candidates that have an above-median utility. When the voter thinks that others are balancing their votes randomly and evenly, the strategy maximizes the voter's power or efficacy, meaning that it maximizes the probability that the voter will make a difference in deciding which candidate wins. Optimal strategic approval voting fails to satisfy the Condorcet criterion and can elect a Condorcet loser. Strategic approval voting can guarantee electing the Condorcet winner in some special circumstances. For example, if all voters are rational and cast a strategically optimal vote based on a common knowledge of how all the other voters vote except for small-probability, statistically independent errors in recording the votes, then the winner will be the Condorcet winner, if one exists. Strategy examples In the example election described here, assume that the voters in each faction share the following von Neumann–Morgenstern utilities, fitted to the interval between 0 and 100. The utilities are consistent with the rankings given earlier and reflect a strong preference each faction has for choosing its city, compared to weaker preferences for other factors such as the distance to the other cities. Using these utilities, voters choose their optimal strategic votes based on what they think the various pivot probabilities are for pairwise ties. In each of the scenarios summarized below, all voters share a common