This reminds me of the Sultan’s Dowry problem.

http://mathworld.wolfram.com/SultansDowryProblem.html

***Begin Quote***

A sultan has granted a commoner a chance to marry one of his n daughters. The commoner will be presented with the daughters one at a time and, when each daughter is presented, the commoner will be told the daughter’s dowry (which is fixed in advance). Upon being presented with a daughter, the commoner must immediately decide whether to accept or reject her (he is not allowed to return to a previously rejected daughter). However, the sultan will allow the marriage to take place only if the commoner picks the daughter with the overall highest dowry. Then what is the commoner’s best strategy, assuming he knows nothing about the distribution of dowries (Mosteller 1987)?

***AND***

The problem is most commonly stated with n==100 daughters, which gives the result that the commoner should wait until he has seen 37 of the daughters, then pick the first daughter with a dowry that is bigger than any preceding one. With this strategy, his odds of choosing the daughter with the highest dowry are surprisingly high: about 37.10% (B. Elbows; Honsberger 1979, pp. 104-110, Mosteller 1987; Havil 2003, p. 136). As the number of daughters increases, this tends towards 1/e approx 36.787…%  (Sloane’s A068985).

***End Quote***

The best thumbnail answer is to listen to about a third and then take the next one that exceeds the highest you’ve heard so far. Not a perfect answer but surprisingly it gets the nod about a third of the time.

So to, the seeker, with an offer in hand, will rarely get a second one to weigh against the offer in hand.

As the inveterate tinkerer, I have some wisdom (I hope it’s wisdom and not barbara striesand) to offer:

(1) I evaluate offers on: (a) actual dollars, (b) commute, (c) “feel”, (d) potential earnings, (e) “potential opportunity”, and (f) “durability”. Being a mathematical kinda fellow, I have established “minimally acceptable” criteria in each dimension.

(2) One dimension doesn’t get to “trump” another dimension. Twice as much money with an arduous commute is not a good trade. I’ve done it I know.

(3) So as not to be labeled “job hopper”, I have to be able to keep the job for at least a year. That looks like two on a resume. That’s durability!

My policy is to take the first offer over the minimum in these six dimensions.

FWIW YMMV
Fjohn