Everyday Failure of Simple Majority Rule

Recently, I polled my roommate group chat on whether or not we should adopt a Russian Tortoise. The result: two resounding “yes” responses and two resounding “no” responses. In a situation where we were all 5 taking collective action via simple majority rule, my third “yes” would have broken the tie, and we would now have a tortoise named Clyde! 

But, imagine that I am a Downsian political party, trying to maximize votes via policy to win office and power— or, to win inter-roommate popularity. I face a conundrum in trying to craft my party "policy," given that there is no median to in my current four person electorate, and no winner under simple majority. If I was competing with some other, external “party” to be the most popular roommate via simple majority rule, and we were trying to appease this specific electorate of four via our tortoise policies, there would be no median vote for us to tailor our policy to and no deciding winner under simple majority rule. Even without parties, in a simple situation with four people taking collective action, majority rule fails to produce a winner in the 2-2 case.

This may seem both trivial and obvious, but this phenomenon could scale up to create serious political issues in the real world! Admittedly, this problem becomes less pronounced in a national election with millions of voters, given that you are probabilistically less-likely to have a race that comes down to a single, median vote. However, even with a massive, 10-trillion-person-sized electorate, the outcome could be 5,000,000,000 votes for “tortoise” and 5,000,000,000 votes for “no tortoise." In this case, neither a "pro-tortoise" or an "anti-tortoise" party could win. It could becomes necessary to scrap the simple majority tenet in order to resort to an alternative decision-making rule... might I propose a new, "tortoise and the Hare" method? Regardless, further economic research should compare the external costs generated by a tortoise litter box and the treatment of tortoises as a public good.