Where to go for dinner?

When my team goes on the road for tournaments, often our coaches let us pick where we go for dinners. For simplicity we usually stick with a simple majority decision. However, a problem arises because within the typical five of us, there are 2 people that primarily like to eat super healthy, 2 people that don’t mind unhealthy food, and 1 person who is somewhere in the middle and can swing either direction. This causes issues as myself being on the extreme of not minding unhealthy food, will not always get my preferred dinner and sometimes end up with a salad for dinner. No matter how much the two sides try to petition our cases to our coaches about our choice of restaurant, it always comes down the middle person, the median voter. 

As we have seen, no matter the distribution of parties in an election, it will come down to the median voter, and each party will shift their policies to appeal to this median voter. We see that even outside of a political realm, the median voter theorem still holds because she is the deciding vote. In the past we have not moved in towards the median voter’s preferences, both sides sticking to our “extremist” point of view, which led to the middle person’s vote being a shot in the dark because of imperfect information. We wouldn’t act rationally and try to edge inward, sticking with our positions of a super healthy place or a super unhealthy place. This was because on any given day we had to guess what kind of food our median voter was in the mood for, and only sometimes would our perceived view of her preferences be the real view. So some days my side would be closer to her real preferences and some days the other side would be closer to her real preferences. But as we have gotten to know each other better, we have understood her preferences better. So with my new knowledge of the median voter theorem, I can now choose a restaurant that fits her preferences slightly better than the other side to convince her to choose our restaurant and we win the vote on a consistent basis.