MATHMEASURE FOR SECURITY DECISIONMAKING UNDER UNCERTAINTY: SECURABILITY

HERE'S THE THE DEAL: As a DECISION-GUIDE, you will be given a FORMULA involving only FRACTIONS to be added and subtracted. If you've WORKED any PROBABILITY problem, you've done the same thing. So the TACTICS haven't changed -- only the STRATEGY, since the PROBABILITY MEASURES refer to EVENTS, while the SECURABILITY MEASURES refer to any TIPOFF. (SECURABILITY relates to any TIPOFF in the way that PROBABILITY relates to any EVENT. Dig?)

And this FORMULA will show that "playing long shorts" CAN PAY OFF BIG! (Something experience can tell you only for limited cases.)

To use it, we'll relabel its TIPOFF and EXCEPTION. No longer "A, B", but, respectively, "T, E" -- "T" for "TIPOFF", "E" for "EXCEPTION" from ROUTINE BEHAVIOR. So it runs:

  • ((T -> E) & E) -> T.
  • T -> E: TIPOFF T implies EXCEPTION E.
  • (...)&P: EXCEPTION E is CONFIRMED or OBSERVED.
  • ((...)&P)ÉT: This implies that T is (possibly) CORRECT. I relabel the TABLES for this:
    TET -> E(T -> E) & E>FONT?((T -> E) & E) -> T
    00101
    01110
    10001
    11111
    However, I admitted that this uses something the Logician labels "FALLACY OF ASSERTING THE CONSEQUENT". However,
    1. FAC FAILS BY JUST ONE CASE OUT OF FOUR.
    2. That single FAILURE QUALIFIES IT TO DEAL WITH REALITY, whereas NO FAILURE (as with MP) TAKES IT OUT OF REALITY AND PUTS IT INTO LANGUAGE!

    So what's so great about this FORM, otherwise?

    Here's a clue of what you'll learn. The LAST TABLE ABOVE DISPLAYS ONLY ONE POSSIBILITY OUT OF FOUR OF THE CONCLUSION BEING UNTRUE.

    The "great stuff" is the "positive part" can get better, with "the negative" remaining CONSTANT.

    1. Suppose that, besides the CONFIRMED EXCEPTION E (now labeled E1), TIPOFF T also implies another EXCEPTION E2 WHICH IS ALSO CONFIRMED.
    2. The FORM becomes ((T -> ((E1 & e2)&(E1&E2)) -> T. Here are the TABLES for this:

      T E1 E2 (E1&E2) T -> (E1 & E2) ((T -> (E1&E2))& (E1&E2) (((T -> (E1&E2))& (E1&E2)) -> T
      0000101
      0010101
      0100101
      0111110
      1000001
      1010101
      1100101
      1111111

      • THE NUMBER OF ROWS (POSSIBILITIES) DOUBLED, from 4 ROWS to 8 ROWS.
      • THE NUMBER OF POSSIBLE FAILURES REMAINED THE SAME, 1 -- NOW 1 OUT OF 8!

      Continuing, if T PREDICTED ONE MORE CONFIRMED PREDICTION.

      • THE POSSIBILITIES WOULD DOUBLE TO 16.
      • with still only 1 POSSIBILITY OUT OF THE 16 OF FAILURE!
      "SUCCESS BREEDS SUCCESS!" As long as THE NUMBER OF CONFIRMED EXCEPTIONS FOLLOW FROM THE SINGLE TIPOFF, the "SCORE" gets BETTER and BETTER. That's the "great thing" about FAC.

      What? You're crying over the work involved in TABLES and READING THEM? Not to worry! I'll give you an SECURABILITY FORMULA, which will calculate ALL IN A MINUTE. And, in another file, I'll give you an SECURABILITY CALCULATOR.

      First, consider BONUSES which follow from THE SECURABILITY FORMULA, PROVIDING A MATHMEASURE FOR SECURITY DECISIONMAKING UNDER UNCERTAINTY.