Are You The One?: The Hardest Perfect Matching Problem Invented
When searching for love, the biggest question many young singles ask themselves is: Are you the one? Applicants to participate on a national reality TV show, “Are You the One?” were used in a dating algorithm that maximizes compatibility using in-depth interviews, questioning, and compatibility testing to determine each person’s “perfect match.” Often there are 10 men and 10 women who live together, socialize, date, and are weekly all tested simultaneously to pick their ideal person. From their pickings, the participants are shown the quantity of perfect matches out of 10, but not the specific perfect pairs. If everyone chose correctly, the show ends and the 20 participants split a cash prize of $1,000,000. This cash prize is necessary to put a valuation on the objective of the game rather than just finding a new dating partner to take home. But on the other hand, the consequence for 0 perfect matches paired up that week is the cash prize getting split in half.
Therein itself lies the problem: if there are between 1 and 9 perfect matches for a given week, an infatuated couple wont entertain the idea of their matching being a false pair, therefore putting all their eggs in one basket by not socializiing with any more potential partners. Rather that, they would instead assume it must be another couple that are mismatched. This wouldn’t be as big of an issue if not for the limited number of 10 weekly tests to find the perfect matching with a likelihood of 1/3,628,800 if chosen blindly. This applies perfectly to our perfect matching concepts in Networks as a perfect matching occurs when all nodes of the graph are paired with one other node of the opposite group. In this case, our main difference being the links representing an algorithm determined soulmate. Which in fact could make this one of the most difficult matching problems due to the subjective, unquantifiable idea of love rather than our typical mundane rating systems of prices or values.
I would say each node of this matching graph could have multiple temporary links representing all the partners that a specific contestant could have a budding relationship with to varying depth. We see in the example matching below that a variety of issues can arise:
- Two people who are perfect matches on paper may end up as platonic in-person. The idea of soulmates does not automatically imply romance.
- An incorrect pairing may be locked in together and ignore other options, causing a cascade affect.
However there is one saving grace that couples can use to verify their perfect match status: The Truth Booth. Once a week, the 20 singles vote to send who they believe to be the strongest and/or most likely pairing to settle the matter once and for all. If the pairing is verified, they are sent to a Honeymoon villa for the remaining singles to mingle without them. Otherise if they are an incorrect match, they are put back into the dating pool to either begrudgingly stay together or finally search for their true match.
https://towardsdatascience.com/solving-mtvs-are-you-the-one-is-it-possible-to-never-lose-992488277099