### Dating math secretary problem

Furthermore, this method should involve some sort of waiting process during which we establish the quality of the potential marriage partners and then determine a stopping rule which tells us who to marry. The basic idea of this optimal policy, or stopping rule, [1] is to date around for a while in order to determine the quality of the possible applicants for marriage. Henceforth, we call this strategy the playing-the-field strategy. Why are we only interested in those two candidates?

We are only interested in those two because our entire strategy revolves around them. We consider three cases: The next part might tend towards the mathematically technical side. In this article, I want to try something new. I write the article in a way that is understandable even if you ignore the mathematical parts. Thus, if you do not feel like following the calculations, you are free to skip the grey parts and you are still able to follow my thoughts conceptually.

## How To Optimize Your Love Life

So far, we have ignored one major aspect concerning the realism of this problem. We are not sure how many partners we have in a lifetime. Not knowing the number of future possible dating partners makes the problem more difficult.

Do you want to buy a house without having to visit every single one that is for sale? Apply the playing-the-field strategy. Do you want to find the best hotel without looking at every single offer on a website?

We can go through the same calculation for and find that. This means you should discard the first person and then go for the next one that tops the previous ones. So you should discard the first two people and then go for the next one that tops the previous ones. These percentages are nowhere near 37, but as you crank up the value of , they get closer to the magic number. There's actually a more rigorous way of estimating the proportion, rather than just drawing a picture, but it involves calculus.

Those who are interested should read this article , which looks at the problem in terms of a princess kissing frogs and has the detailed calculations. The magic number 37 turns up twice in this context, both as the probability and the optimal proportion. This comes out of the underlying mathematics, which you can see in the article just mentioned. That's not great odds, but, as we have seen, it's the best you can expect with a strategy like this one. So should you use this strategy in your search for love? Sadly, not everybody is there for you to accept or reject — X, when you meet them, might actually reject you!

Like all mathematical models our approach simplifies reality, but it does, perhaps, give you a general guideline — if you are mathematically inclined. Our dating question belongs to the wider class of optimal stopping problems — loosely speaking, situations where you have to decide when is the right time to take a given action go for a relationship after having gathered some experience dated some people in order to maximise your pay-off romantic happiness. Life abounds with these kind of problems, whether it's selling a house and having to decide which offer to take, or deciding after how many runs of proofreading to hand in your essay.

Marianne Freiberger is Editor of Plus. What is the best strategy if you try to maximise the expected rank-order score of the person you choose, rather than the probability of getting the very best? You can se emore of the maths in this article: Under the assumption that success is achieved if and only if all the selected candidates are superior to all of the not-selected candidates, it is again a problem that can be solved. This leads to a strategy related to the classic one and cutoff threshold of 0.

Experimental psychologists and economists have studied the decision behavior of actual people in secretary problem situations.

This may be explained, at least in part, by the cost of evaluating candidates. In real world settings, this might suggest that people do not search enough whenever they are faced with problems where the decision alternatives are encountered sequentially.

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For example, when trying to decide at which gas station along a highway to stop for gas, people might not search enough before stopping. If true, then they would tend to pay more for gas than if they had searched longer. The same may be true when people search online for airline tickets.

Experimental research on problems such as the secretary problem is sometimes referred to as behavioral operations research. While there is a substantial body of neuroscience research on information integration, or the representation of belief, in perceptual decision-making tasks using both animal [3] [4] and human subjects, [5] there is relatively little known about how the decision to stop gathering information is arrived at.

Researchers have studied the neural bases of solving the secretary problem in healthy volunteers using functional MRI.

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Decisions to take versus decline an option engaged parietal and dorsolateral prefrontal cortices, as well ventral striatum , anterior insula , and anterior cingulate. Therefore, brain regions previously implicated in evidence integration and reward representation encode threshold crossings that trigger decisions to commit to a choice.

### The secretary problem and realism

The secretary problem was apparently introduced in by Merrill M. He referred to it several times during the s, for example, in a conference talk at Purdue on 9 May , and it eventually became widely known in the folklore although nothing was published at the time. In he sent a letter to Leonard Gillman , with copies to a dozen friends including Samuel Karlin and J. Robbins, outlining a proof of the optimum strategy, with an appendix by R. Palermo who proved that all strategies are dominated by a strategy of the form "reject the first p unconditionally, then accept the next candidate who is better".

He had heard about it from John H. Gerald Marnie, who had independently come up with an equivalent problem in ; they called it the "game of googol". Fox and Marnie did not know the optimum solution; Gardner asked for advice from Leo Moser , who together with J. Pounder provided a correct analysis for publication in the magazine. Soon afterwards, several mathematicians wrote to Gardner to tell him about the equivalent problem they had heard via the grapevine, all of which can most likely be traced to Flood's original work. Ferguson has an extensive bibliography and points out that a similar but different problem had been considered by Arthur Cayley in and even by Johannes Kepler long before that.

The secretary problem can be generalized to the case where there are multiple different jobs. When a candidate arrives, she reveals a set of nonnegative numbers. Each value specifies her qualification for one of the jobs.

## Secretary problem - Wikipedia

The administrator not only has to decide whether or not to take the applicant but, if so, also has to assign her permanently to one of the jobs. The objective is to find an assignment where the sum of qualifications is as big as possible. Thus, it is a special case of the online bipartite matching problem. From Wikipedia, the free encyclopedia. Algorithms — ESA Lecture Notes in Computer Science. Retrieved from " https: Decision theory Sequential methods Matching Optimal decisions Probability problems Mathematical optimization in business.