Methodology:Making social sciences more scientific

Rein Taagepera Predictive Vs Postdictive models

The major goal of sciences is to explain in a way that can lead to prediction:

“this should be so, because logically ...” instead of

“this is so, an that’s it”

The purely postdictive approach reverses the usual role of scientist and statistician,

and crowds out creative thinking

Features for the construction of a quantitatively predictive model

• to use boundary conditions and other logical constraints to establish anchor points;

• to look for simplest set of equations that does not violate the logical constraints;

• to wonder about the possible range of values of coefficients and constants (some limits are firm other are fluid);

• to use the means of data to estimate some coefficients in the predictive model (still a step that precedes regression)

V = electoral volatility More parties (N) ?V = f (N)More N More choice for switching More VdV / dN >0 (directional logical model)How to measure N?N = 1/∑ (si)2 comparing two elections for V, average of N

What would you do next?

DataOLSV = a + bN b=dV/dN positive and significantR2

Sherlock Holmes (eliminate the impossible) 0 ≤ V ≤ 100 N ≥ 1 (+ assump. at least one party gets votes in both elections)

Conceptual extreme case (1,0) anchor N=1 V=0If V = a + bN 0 = a+b a = -bV = -b + bN = b(N-1)Surprise area eg N=6 & V=100% 100=b(6-1) b=20Without any further information betw. V=0 e V=20(N-1)

In absence of any other guess, the best guess is the average of the likely extremes V=10(N-1)The range of the prediction remains high, but it is still better than a simple directional model (dv/dN>0) which accepts any positive slope Eg. predictions for N = 4The second one is a quantitative predictive model , Though not deterministic (+/-30)Only here come dataBut we don’t need a regression, but only averagesIf V=b(N-1) b = mean V / (mean N-1)(Heat 2005) Indian state dataset Mean N = 3.65; Mean V = 31.6 b = 11.9 V = -11,9+11,9N (Heat found through OLS V = -9.07 +11.14N (the fit is similar)

Refining…Whenever N>9.34 V would surpass 100%«But predictive models cannot violate logic even under extreme conditions»Non linearity models like dy/dx=k(C-y) where C is the ceiling (100%)

Knowing the refined model one knows if he can use the simplified one

How good my prediction?V = (12+/- ε)(N-1)If we estimated V from 1 Indian election the result could be from 1.4 to 21.4 i.e. 12+/- 10For many elections in roughly the same conditions a rule of thumb would suggest an error equal to the cubic root of 10 ≈ 3V = (12 +/-3) (N-1) as a Universal quantitative prediction

How predictive and postdictive models works

Most numbers published in political science are dead on arrival

Conclusions

Conceptual building has to be brought back in political science

Political Science has to widen the tool-kit complementing passive postdictive models with creative predictive ones