Matchmaking 101

You know, there is a conjecture that a solution must exist, for any arbitrary’ n’ couples” I told her, without a trace of posturing.
“A ‘conjecture‘ is there?” She feigned salon-intellectual pomposity, and then laughed.
“That’s what we have to call it, Sweetheart, ’til it’s been proven” I explained.
“So nu, prove it already..” This time it was the spoiled princess voice.
    We were sitting and eating breakfast, me and my one-and-only, love-of-my-life, imprinted on my limbic-system, thank god I found you, Girl. Million-dollar -a-slice Icelandic salmon with genuine Philadelphia cream cheese, delivered by hand-picked-for-their-brotherly-love couriers fresh each morning. Yes nothing’s too good for her Chosen One. And we were planning a small party, twenty guests:  ten guys and ten girls. Decor, cuisine, entertainment, all these had been quickly settled; we hardly ever disagree on anything. But seating? She was concerned that one or more of the guests might be troubled over having to sit opposite his or her god-forbid ‘second choice’. I let myself ponder a second the  mathematics of the challenge, and remembered having read something long ago, germane to the issue. Ok, I probably could have stated it in a more ‘plain-folks’ style, but she actually likes jargon, (and everything else about me, did I mention that?).
“Ok, well… um… let’s see…” I started.
“That’s a proof?” she asked, feigning innocence. I just love her.
“No, pussy-cat, I’m just warmimg up. Now here we go: Each guy can rank-order the girls in preferential order, right? …assign each one a number from one to ten.”
“As can the girls, obviously..”
She handed me another slice of salmon.
“Obviously. I was getting to that. So we now have an array of hope…” I paused a second for her smile  and lost my train of thought, as I considered jumping on a new one.
“So we can create a matrix, like this one:” I quickly drew a chart on a notepad

matrix . My Valentine took one look and reached around behind her to boot the nearest computer, “I think if you plan to submit this to the Journal of Theoretical Matchmaking, you’d better..”
“You’re right”,
I said, grabbing my Bolivian coffee and setting up at the new mission-control position. A few seconds later I had a sample matrix staring at us, waiting for the starting gun:

“Great!” oozed Sweetie-pie, kissing the back of my neck. “Everybody’s happy.”
I hated to disappoint her, but rigour is rigour, and our proof, at least, was still in the fore-play stage.
“No, they just know what they want; we gotta help ’em get it. We need a procedure, see..” I thought of all those dumb ice-breaker party games that lesser-lights seemed to think we needed in order to ‘mix’, back in the Stone Age. Like giving you the name of a food, and you had to find the girl with the animal that ate it. I always got a carrot, which never went with my Sears sweater.
“Well, we could first line them up in two rows, across from each other, on the lawn.” I thought that’d be

“Unless it rains”, she pointed out a flaw in the logic.
“Ok, assume a perfect world. We pick Guy one, he looks at his chart, and walks toward his first choice girl..”
“…who becomes immediately very ill..” She laughed at her intuitive grasp of reality. Women think of everything.
” Ok, maybe she wanted Guy Nine, who am I to legislate morality? So we’ll let her go to that dumb Guy Nine,nu..”
“..who becomes immediately ‘very ill”
She was repeating herself.
“So how would you do it, Miss Einstein?” I really didn’t have a plan, tell the truth, plus I get a free point for respecting her opinion, don’t I?
“Math, Johnny. ..’the uncanny efficiency of math’, you know, Wigener?”
I let Dream Girl take my place at the keyboard while I attempted to get a couple eggs not to ‘marry‘ the teflon skillet. By the time they were on the table she had made some admirable headway:

“What’s up with Girl Three, you know, Miss ‘Na-na-na-na’?” I had to ask.
“She don’t like guys, I guess..” Cutie said ,slyly. As if God almighty had filled in the chart on Mt. Sinai.
“Just great! Replace her. In the name of science.” I decreed, imperiously.” And it kinda looks like Girl Two’s a real knock-out, huh?”
“Dat’s life, kid.”
my co-conspirator informed me, again washing her hands of responsibility. “We do want a realistic model, right?”
“We want a killer party, first, and to get this thing past peer-review of course. Ok, we’ll invite ‘Foxy’, but let’s fudge some choices for Sappho, ok?”
I still had no idea how to stage-manage the thing. I took a deep breath:
“We need a procedure, an algorithm, if you will..”
“I will”
Silly girl.
“..which specifically excludes the possibility that Girl Four, for example, sitting across from Guy Seven, will start to play footsy with Guy Nine, sitting next to him, leaving Guy Seven to try to schmooze Girl One, who make become..”
“Violently ill?”
I laughed at her little obsession with…um.. ‘puke’. “You know what I mean, though, right?”
“Oof! This is like, a simultaneous equation of 100 variables. Can’t we collapse it somewhere?”
she wanted to ‘finish math’ as much as I did. And both of us more than Bertrand Russell. We looked at the charts, scratching our heads in loving unison……

(to be continued, when I get His Meerness, to whom I’m indebted for this puzzle, to reveal the solution. At least I’m honest, haha)


5 thoughts on “Matchmaking 101

  1. Meerness

    I can’t believe you wrote a post about this puzzle! Funny how we can both be talking about the same thing, yet you make it at once interesting and amusing while I just spill out the details…The algorithm is quite simple. First, let every guy go straight to the first girl on his list (“Hubba hubba!”). Odds are, some girls will be left guyless (but don’t worry, girls, you’ll be paired up in no time), and some girls will have more than one guy (that ‘two’ girl, for instance, seems to have attracted quite a group). Those girls will simply choose the guy highest up on their list, and shun the others. The rejected men will cross off that girl’s name from their lists (“What was I thinking? She’s nothing but a slut anyway!”). Then all the rejected guys move to the next girl on their lists, and the process repeats until everyone is happy.The final arrangement (which will be, of course, stable,) will be optimal for the men and not-quite-so-optimal for the women. The question is, who are you trying to please with this party? Worst comes to worst, you can run the algorithm the other way around, risking one of the guys getting violently ill…

  2. elgan

    Just from looking at the top preferences, everyone is doomed to disappointment. Not a single guy and girl chose each other as their first choice. That would be a truly ideal world, nu?

  3. jsolberg

    RS: it’s fiction, you’ve heard of it.
    elgan: Yes, I made sure that would be the case, so as not to cause the Gods to become jealous.
    and finally: Meerness, Yipee… I couldn’t have dreamed of a more helpful and perfectly worded “clue”, (I’ll try to sneak through the light calling it that). In fact, your procedure was my next step, but I tortured myself with the girl/boy/happiness inequality bug. I’m thinking that if I ‘rotate’ the matrixes, that is, list it as ‘points-per-girl’ so to speak, I can apply a formula which maximizes ‘pleasure’ irrespective of gender, by approaching the highest sum total of collective points. Then all I need is the budget for the party, oh, and a luscious co-hostess. Thanks again for your help, v’col ha’cavod l’cha, gever  

  4. livingepitaph

    There is always the “rotation” possibility. One seating arrangement per course. A “musical chairs” sort of thing. This would also cover the potential hazard that the person one may have picked as choice in the onset proved to be a disappointment.


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