## Tuesday, July 16, 2019

### Hiring a secretary

Suppose you ran an insurance office in a small town. Doris, your secretary of thirty-seven years retired and you want to hire a replacement.

You have little idea about the talent pool available. You have been told that the market varies wildly from one location to the next and it also varies through time. You placed an ad and have a number of candidates. How do you know which one to hire?

This problem comes up in all kinds of selection scenarios, including looking for a wife/husband or a used vehicle.

There is even an entry in Wikipedia:

...an administrator who wants to hire the best secretary out of ${\displaystyle n}$ rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled...The difficulty is that the decision must be made immediately.
The optimal stopping rule prescribes always rejecting the first ${\displaystyle \sim n/e}$ applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far
For small numbers

The optimal thresholds r and probability of selecting the best alternative P for several values of n are shown in the following table.

Finding and checking out vehicles is expensive from a time standpoint. I figure it takes between 90 and 120 minutes to drive to the site, find the vehicle and then go through the checklist Belladonna pulled off the internet.

If it is just Belladonna and I, that is four man-hours. If we want to have the vehicle checked out by a mechanic, then the hours and dollars invested in each candidate goes up.

#### 7 comments:

1. Are you ( Or Bella) checking online reviews of the dealers she/you end up going to ? ? Ok, first disclaimer...every dealer has at least a couple of haters ! However, true crooks often get the same negative reviews over and over. Reviews that sound just like...hey, just sold that one but I have a different one that's better. Could save time to check reviews and weed those out.

1. Yes. We started doin that after she found three candidates at a dealership that was rated one if five stars. Bella bought a car yesterday and the dealership rated 4.3 of five.

2. But those hours pay off in the long(er) run, with a vehicle that works for her, which will cause her to want to keep it in good shape.

3. Could be worse. I totaled my truck last winter and the nearest dealers are 200 miles away and I would have had to get a ride to town to check out what looked good on line. Finally decided to put the \$500 in my old truck that we had relegated to haul water, to make it road worthy and hold on to the insurance pay out for a later time.

4. The way I always look at it - similar to Howard's approach - is to accept a period of hardship and put things in place to allow time to increase the probability of a good opportunity to come along. Time favors those with the grit to accept this hardship, and a little preparation can ease its impact on the day-to-day. Have your checked with the older people who make up your community and also asked them to reach out and check outside with others of their age group? There might just be a codger or codgette who is done with driving for whatever reason and has a cream puff to offer for a fair price. Good Luck! I hope your opportunity comes quickly.

5. I am tangential on this but "Who: The A Method of Hiring" By Street and Smart tells you to think through just what you are looking for. Just like when I told my friend "I want to marry a woman with blue eyes that likes herself". Then your friend (friend in the fullest sense) sets you up on a blind date. You have to get past the bling and figure out what is really important. And an aside to my aside is the second qualification is really tough to find.

6. As to hiring, I would interview all of them and pick the best two. Start them at part time and after a week or so you will know which one fits the best and in the interim you keep the pressure up for both to display the talents they possess.

As to a car. Time is your ally. I have never seen 'the lowest price ever' not magically reappear or that the price was a come on and not real. Figure out what you want and then wait until the deal you can live with and is the most favorable comes along. I know being without a vehicle is a pain but rushing to buy something for any reason is not a good idea and you usually bet burnt.