Redefining Rationality The Standard Definition Is Self-Defeating: Diagnosis and Correction

Wedemonstratethatthestandardformalizationofrationality(RStd,Cournot
1838,Nash1950)doesnotsatisfytheintuitivecriterionitclaimstoformalize—“I
wantwhatisbestforme” (RA)—andidentifythereasonthisfailureisnecessary
andgeometric.Theargumentproceedsinthreesteps.
First,RStdoperateswithinarestrictedspaceof formulable functions—the
individualperspectiveFindiv—whichrenders itsownscopeassumptioninvisible
fromwithin. Theonlyobject thatwouldreveal thescope{i}asarestrictionis
e∈EWe(a),whichbelongstoFsist\Findiv: notasarejectedalternative,butasan
objectnotformulablefromthatspace.Withoutaformulablealternative, thescope
{i}cannotappearasachoice—itappearsastheverynatureofrationalanalysis.
Second,Nash(1950)providesevidenceof the failure: whenallagents follow
RStd, theequilibriumaNE isnotPareto-optimal inthegeneral case(gameswith
PriceofAnarchygreaterthan1).Thereasonisgeometric: thefirst-orderconditions
ofRStd zeroout∂Ui/∂ai but remainstructurallyblindto e̸=i∂We/∂ai. Since
Findiv⊊Fsist, nosetof constraintsonRStd canreproduce the systemicPareto
conditions: constraintsnarrowthesearchspacewithoutchangingthegeometrythat
determineswhichsolutionsarereachable.
Third,thecorrectionistochangethegeometry: fromthesystemicperspective
Fsist⊋Findiv,systemicrationality
RS: a∗=argmax
a∈Ae∈E
We(a)
correctly formalizesRA. The sumoperatesover individual andexplicitwelfare
functions—notoveranaggregate—andselectsinP∗ (Lemma5.2).UnderRosen’s
(1965)conditions, theequilibriumwhereall agents followRS coincideswiththe
socialoptimumwithoutexternalplannerandwithoutmechanism.