SPORTS FANS AND ECONOMISTS AND POLITICAL SCIENTISTS PLAY "SCISSORS-PAPER-ROCK"

Sports games and the fields of Economics and Political Science depend upon two critical RELATIONS.

Much of mathematics is comprehended under the notion of RELATIONS (discussed elsewhere at this website), modeled on the BINARY RELATION.) These are the RELATIONS of COMPETITION and PREFERENCE.

In SPORTS, the primary relation is COMPETITION. In ECONOMICS and POLITICS, it is PREFERENCE.

In ECONOMICS, SELLERS COMPETE and BUYERS SHOW PREFERENCE for this PRODUCT of a SELLER or that. In POLITICAL SCIENCE, REPRESENTATION CANDIDATES COMPETE and VOTERS SHOW PREFERENCE for this CANDIDATEor that.

The PROBLEM for SPORTS FANS and ECONOMISTS and POLITICAL SCIENTISTS is that -- UNLIKE THE CRITICAL NOTIONS IN OTHER SUCCESSFUL SCIENCES -- THESE SUPPORTING RELATIONS for ECONOMICS and POLITICAL SCIENCE are only QUASI-TRANSITIVE (only a "sometime thing"), which means that TRYING TO DECIDE MAKES YOU RUN IN CIRCLES, like a poor old dog chasing his tail!

Competition is only quasi-transitive

Competition between individuals or teams or organizations or nations is supposed to put those involved into a RANKING ORDER: First, Second, Third, ettsettery. Righteous?

Wrongeous! as we can readily show by a figure&ground test (a subject more thorougly discussed elsewhere at this website). How do we do that test? Ah!

I'll illustrate by a kid's game which, likely, you know. "Scissors-Paper-Rock". Competitors shake fists three times, then finger-form ONE of THREE shapes:

  1. forefinger and middle-finger extended denote "Scissors";
  2. flat out hand denotes "Paper";
  3. closed fist denotes "Rock".

And the results?

  1. Since "Scissors cuts Paper", the "Scissors"-person may wrist-slap the "Paper"-person;
  2. since "Paper covers Rock", the "Paper"-person may wrist-slap the "Rock"-person;
  3. since "Rock breaks Scissors", the "Rock"-person may wrist-slap the "Scissors"-person.

But this means that -- THEORETICALLY, IN THE LONG RUN -- NO ONE WINS! For, if ">" denotes "beats" or "dominates", we have: SCISSORS > PAPER > ROCK > SCISSORS > PAPER > ROCK > .... Etsettery.

TRANSITIVE BREAKS DOWN! THE RELATION IS INTRANSITIVE!

Similar to King Arthur's Round Table! As King Arthur intended, no knight dominated since no one was highest at the Table!

But TRANSITIVITY IS THE NECESSARY CONDITION FOR ORDER! FAILURE OF TRANSITIVITY DESTROYS ORDER AND MAKES A MOCKERY OUT OF COMPETITION!

Let's formulate this mathematically, as follows:

  1. We take the MINIMAL mathematical condition for an ORDERING RELATION as our FIGURE. (If this CONDITION fails, the RELATION IS NOT AN ORDERING RELATION!)

  2. We take COMPETITION, as he blows in sports or marketing or political competition or whatever, as our GROUND. (Okay?)

  3. We put the FIGURE OF AN ORDER RELATION against the GROUND OF COMPETITION -- FOR EVERY KIND OF CASE. (Still with me? Ok. Don't let that "EVERY" worry you. One case is going to decide the "game".)

  4. We see if FIGURE MATCHES GROUND. (Charlotte?)

  5. Finally, we PASS JUDGMENT:
    1. IF WE FIND ONE CASE WHEREIN THE FIGURE OF ORDER RELATION MATCHES THE GROUND OF COMPETITION, AND ONE CASE WHEREIN IT FAILS TO MATCH, then WE JUDGE THAT COMPETITION IS ONLY A QUASI-ORDERing RELATION, but cannot be trusted as AN ORDERING RELATION -- doing the "job" we wish it to do;
    2. if WE CAN'T FIND A FAILURE or WE CAN'T FIND A SUCCESS, then the matter is MOOT and OPEN TO FUTURE REVELATIONS.

    Righteous? "Hey! Whut's uh Minnie-mull kondishun? enyhow?"

    Patience! I'll show you that minimal condition for an ordering relation and show that it provides an easy test or indicator.

    Mathematicians can show that a relation cannot ORDER a set or system or structure if it fails to be TRANSITIVE.

    And you know what that means. Sure you do! For example, "Things equal to the same thing are equal to each other." Remember? (Or were you talking when Teacher told you this?)

    In general, let "R" denote a relation, and let a, b, c stand for relata to be combined by relation R. And suppose we know that a R b ("relatum a has relation R to relatum b"). And we further know that b R c ("b has the same relation R to c").

    Now, we ask the relational question a R c ? ("does a have relation R to c?"). If "Yes", then R fulfills the minimal requirement for an ordering relation -- even if only a poor man's ordering relation. But, if "No", then forget it! And that minimal requirement is called "transitivity" (roughly, the first two conditions transfer or transit the property along the line to the third).

    Well, if you weren't talking in class the day Teacher went over this, you''ll remeber that, when a = b, and b = c, it follows that a = c. So equals, which is a special case of equivalence (for example, congruence in geometry is an equivalence relation) is transitive. And so is another relation you learned in arithmetic: less thandenoted "<". If, for numbers p, q, r, we have p < q and q < r, then we know that p < r. The "less than" (which mathematicians call a "total ordering relation") is also transitive.

    Now, we're ready to apply the FIGURE of the transitive test to the GROUND of COMPETITION.

    Have you ever observed a case where, after Team A beat Team B and then Team B beat Team C, it also happened that Team A beat Team C? Sure! (Otherwise, get a life!) But have you ever noticed a case where this failed? That is, after A beat B and B beat C -- doggone it! -- C turned around and beat C. Oh yeeeeaaaahhh! Read 'em and weep!

    That jimdandy MEASURE OF COMPETITION is only a QUASI-ORDERING RELATION -- a QUASI-MEASURE -- after all.

    And this means that investing in SPORTS or ECONOMIC or POLITICAL ACTIVITY involves some GAMBLING, UNLESSSSSS:

    1. you can FIX THE GAME;
    2. or FIX THE ELECTION;
    3. or MONOPOLIZE OR OLIGOPOLIZE THE MARKET.

    Happy questing