Our task is to show that the best value of corresponds to 37% of .We’ll do that by calculating the probability of landing X with your strategy, and then finding the value of that maximises this probability.
Before we start, here’s a picture of the end result.
It shows the values of on the horizontal axis and the best value of , the one that maximises the probability of ending up with X, on the vertical axis.
came out, essentially warning women that the only surefire way to land a guy was to fasten your chastity belt, shut up, and wait for him to pursue you. Among the 35 rules were grave warnings: "Don't Talk to a Man First (and Don't Ask Him to Dance)," "Don't Talk Too Much", and "Don't Live with a Man." Basically, authors Sherrie Schneider and Ellen Fein stopped just short of suggesting your dad offer your fiancé a dowry of 40 goats and 20 cows.
Despite these antiquated , we Cosmo girls survived the past 17 years freely opening our mouths, hitting on guys, living with them, asking them to dance, and—gasp–having sex (earmuffs, Sherrie and Ellen: Sometimes on the first date! Lucky for us, , enlightening us on how (not) to date in light of texting, sexting, Facebook, Match, and JDate!
Sadly, a person you have dated and then rejected isn’t available to you any longer later on.
Among your pool of people, there’s at least one you’d rate highest.
If X is the person you date, you’re in luck: since X is better than all others so far, you will pick X for sure. If X is the person you date, you’ll pick them to settle down with as long as the person and the person both didn’t have a higher rating than the ones you saw before them. Therefore, We can continue like this until we hit the case in which X is the last person you date.
Therefore, If X is the person, you’ll pick them to settle down with as long as the person didn’t have a higher rating than all the previous people. In other words, you pick X if the highest-ranked among the first people turned up within the first people. You will pick X as long as the , , etc, and people all didn’t have a higher rating than the ones you saw before them. Therefore, This means you should discard the first person and then go for the next one that tops the previous ones.
For twenty potential partners () you should choose , which is 35% of . For a hundred potential partners () you should choose (that’s obviously 37% of ) and for (an admittedly unrealistic) 1000 () you should choose , which is 36.8% of .