(* Afriat's Efficiency Index *)



rdEMatrix[p_, x_, e_] := Module[{i, j, n},

    n = Length[p];

    Table[

      If[(e p[[i]].x[[i]] >= p[[i]].x[[j]]) || i == j, 1, 0], {i, 1, n}, {j, 

        1, n}]]



tClosure[m_] := Sign[MatrixPower[m, Length[m]]]



GARPOK[p_, x_, m_, e_] := Module[{i, j, n},

    n = Length[m];

    Table[

      If[m[[i, j]] == 1 && (e p[[j]].x[[j]] > p[[j]].x[[i]]), False, True],

      {j, 1, n}, {i, 1, n}]]



ViolationList[p_, x_, e_] := Module[{m},

    m = tClosure[rdEMatrix[p, x, e]];

    Union[Flatten[Position[GARPOK[p, x, m, e], False]]]]



NumberViolations[p_, x_, e_] := Length[ViolationList[p, x, e]]



p = {{1., 2.}, {2., 1.}}; x = {{1., 2.}, {2., 1.}};



MatrixForm[GARPOK[p, x, tClosure[rdEMatrix[p, x, .81]], .81]]



MatrixForm[GARPOK[p, x, tClosure[rdEMatrix[p, x, .79]], .79]]



AfriatEfficiency[p_, x_, maxSteps_] := Module[{step, e}, e = 1/2;

    For[step = 1, step <= maxSteps, step++,

      If[NumberViolations[p, x, e] > 0, e = e - 2^(-(step + 1)), 

        e = e + 2^(-(step + 1))];

      Print[N[e]]]]