The model is built in a way that it could happen that the outcome does not reflect the preference of the median voter even though they are able to anticipate the decision of the elected citizen. The reasons why this might happen are the following. First, there may be an equilibrium with two candidates who, if elected, will implement decisions that are symmetric around the median voter, but relatively far away from the median voter's preferred position. Second, parameters might be such that, without reservation, there is no equilibrium in which a woman is a candidate. In this case, the policy implemented will be on the right of the most 'pro-women' outcome preferred by a man (on the right of the median voter). Third, if the preferences between men and women do not overlap and the preferences of the lobbies are sufficiently biased towards men preferences, it is possible that any policy outcome will be to the right of the median voter's preferred outcome.
In any of these cases, the reservation policy moves the range of outcomes that can be implemented in equilibrium (and improve the median voter's utility).
Nextly, the authors analyze women's decision to run for office when there is no reservation by setting the following propositions: