(* The Transitive Closure of a Preference Relation *)



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

    n = Length[x]; 

    Table[If[p[[i]].x[[i]] >= p[[i]].x[[j]], 1, 0], {i, 1, n}, {j, 1, n}]]



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



p = {{1, 2, 8}, {4, 1, 8}, {3, 1, 2}};

x = {{2, 1, 3}, {3, 4, 2}, {2, 6, 2}};



m = rdMatrix[p, x]



tClosure[m]



(* Checking GARP *)



ObsRP[i_, m_] := Complement[

    Table[If[m[[i, i]] > 0, j, i], {j, 1, Length[m]}], {0}]



consEfficiency[p_, x_] := Module[{m, n},

    m = tClosure[rdMatrix[p, x]];

    n = Length[x];

    Table[Min[x[[ObsRP[i, m]]].p[[i]]/p[[i]].x[[i]]], {i, 1, n}]]



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

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



consEfficiency[p, x]