// build the square matrix of position utilities.
// Row is actor i, Column is position of actor j,
// U(i,j) is utility to actor i of position of actor j.
// If there are duplicate positions, there will be duplicate columns.
void RP2State::setAllAUtil(ReportingLevel) {
const unsigned int na = eMod->numAct;
assert(Model::minNumActor <= na);
assert(na <= Model::maxNumActor);
aUtil = {};
aUtil.resize(na);
auto uMat = KMatrix(na, na); // they will all be the same in this demo
for (unsigned int j = 0; j < na; j++) {
unsigned int nj = posNdx(j);
auto utilJ = actorUtilVectFn(-1, nj); // all have objective perspective
for (unsigned int i = 0; i < na; i++) {
uMat(i, j) = utilJ[i];
}
}
for (unsigned int i = 0; i < na; i++) {
aUtil[i] = uMat;
}
return;
}
// return the list of the most self-interested position of each actor,
// with the CP last.
// As a side-affect, set each actor's min/max permutation values so as to
// compute normalized utilities later.
vector<VUI> scanAllPossiblePositions(const RPModel * rpm) {
unsigned int numA = rpm->numAct;
unsigned int numRefItem = rpm->numItm;
assert(numRefItem == rpm->numCat);
LOG(INFO) << "There are" << numA << "actors and" << numRefItem << "reform items";
KMatrix aCap = KMatrix(1, numA);
for (unsigned int i = 0; i < numA; i++) {
auto ri = ((const RPActor *)(rpm->actrs[i]));
aCap(0, i) = ri->sCap;
}
LOG(INFO) << "Actor capabilities: ";
aCap.mPrintf(" %.2f ");
LOG(INFO) << "Effective gov cost of items:";
(rpm->govCost).mPrintf("%.3f ");
LOG(INFO) << "Government budget: " << rpm->govBudget;
assert(0 < rpm->govBudget);
string log("Value to actors (rows) of individual reform items (columns):");
for (unsigned int i = 0; i < rpm->actrs.size(); i++) {
auto rai = ((const RPActor*)(rpm->actrs[i]));
for (unsigned int j = 0; j < numRefItem; j++) {
double vij = rai->riVals[j];
log += KBase::getFormattedString(" %6.2f", vij);
}
}
LOG(INFO) << log;
LOG(INFO) << "Computing positions ... ";
vector<VUI> allPositions; // list of all possiblepositions
VUI pstn;
// build the first permutation: 0,1,2,3,...
for (unsigned int i = 0; i < numRefItem; i++) {
pstn.push_back(i);
}
allPositions.push_back(pstn);
while (next_permutation(pstn.begin(), pstn.end())) {
allPositions.push_back(pstn);
}
const unsigned int numPos = allPositions.size();
LOG(INFO) << "For" << numRefItem << "reform items there are"
<< numPos << "positions";
// -------------------------------------------------
// The next section sets up actor utilities.
// First, we compute the unnormalized, raw utilities. The 'utilActorPos' checks
// to see if pvMin/pvMax have been set, and returns the raw scores if not.
// Then we scan across rows to find that actor's pvMin/pvMax, and record that
// so utilActorPos can use it in the future. Finally, we normalize the rows and
// display the normalized utility matrix.
auto ruFn = [allPositions, rpm](unsigned int ai, unsigned int pj) {
auto pstn = allPositions[pj];
double uip = rpm->utilActorPos(ai, pstn);
return uip;
};
LOG(INFO) << "Computing utilities of positions ... ";
// rows are actors, columns are all possible positions
auto rawUij = KMatrix::map(ruFn, numA, numPos);
// set the min/max for each actor
for (unsigned int i = 0; i < numA; i++) {
double pvMin = rawUij(i, 0);
double pvMax = rawUij(i, 0);
for (unsigned int j = 0; j < numPos; j++) {
double rij = rawUij(i, j);
if (rij < pvMin) {
pvMin = rij;
}
if (rij > pvMax) {
pvMax = rij;
}
}
assert(0 <= pvMin);
assert(pvMin < pvMax);
auto ai = ((RPActor*)(rpm->actrs[i]));
ai->posValMin = pvMin;
ai->posValMax = pvMax;
}
LOG(INFO) << "Normalizing utilities of positions ... ";
KMatrix uij = KBase::rescaleRows(rawUij, 0.0, 1.0); // von Neumann utility scale
string utilMtx("Complete (normalized) utility matrix of all possible positions (rows) versus actors (columns) \n");
for (unsigned int pj = 0; pj < numPos; pj++) {
utilMtx += KBase::getFormattedString("%3u ", pj);
auto pstn = allPositions[pj];
//printVUI(pstn);
utilMtx += KBase::stringVUI(pstn);
utilMtx += " ";
for (unsigned int ai = 0; ai < numA; ai++) {
double uap = uij(ai, pj);
utilMtx += KBase::getFormattedString("%6.4f, ", uap);
}
utilMtx += KBase::getFormattedString("\n");
}
LOG(INFO) << utilMtx;
// -------------------------------------------------
// The next section determines the most self-interested positions for each actor,
// as well as the 'central position' over all possible reform priorities
// (which 'office seeking politicans' would adopt IF proportional voting).
LOG(INFO) << "Computing best position for each actor";
vector<VUI> bestAP; // list of each actor's best position (followed by CP)
for (unsigned int ai = 0; ai < numA; ai++) {
unsigned int bestJ = 0;
double bestV = 0;
for (unsigned int pj = 0; pj < numPos; pj++) {
if (bestV < uij(ai, pj)) {
bestJ = pj;
bestV = uij(ai, pj);
}
}
string bestMtx("Best position for ");
string ais = std::to_string(ai);
//string bjs = std::to_string(bestJ);
string ps = KBase::stringVUI(allPositions[bestJ]);
bestMtx += ais + " is " + ps;
LOG(INFO) << bestMtx;
//LOG(INFO) << "Best for" << ai << "is ";
//printVUI(positions[bestJ]);
bestAP.push_back(allPositions[bestJ]);
}
LOG(INFO) << "Computing zeta ... ";
KMatrix zeta = aCap * uij;
assert((1 == zeta.numR()) && (numPos == zeta.numC()));
LOG(INFO) << "Sorting positions from most to least net support ...";
auto betterPR = [](tuple<unsigned int, double, VUI> pr1,
tuple<unsigned int, double, VUI> pr2) {
double v1 = get<1>(pr1);
double v2 = get<1>(pr2);
bool better = (v1 > v2);
return better;
};
auto pairs = vector<tuple<unsigned int, double, VUI>>();
for (unsigned int i = 0; i < numPos; i++) {
auto pri = tuple<unsigned int, double, VUI>(i, zeta(0, i), allPositions[i]);
pairs.push_back(pri);
}
sort(pairs.begin(), pairs.end(), betterPR);
const unsigned int maxDisplayed = 720; // factorial(6)
unsigned int numPr = (pairs.size() < maxDisplayed) ? pairs.size() : maxDisplayed;
LOG(INFO) << "Displaying highest" << numPr;
for (unsigned int i = 0; i < numPr; i++) {
auto pri = pairs[i];
unsigned int ni = get<0>(pri);
double zi = get<1>(pri);
VUI pi = get<2>(pri);
string ps = KBase::stringVUI(pi);
LOG(INFO) << KBase::getFormattedString(" %3u: %4u %.2f %s", i, ni, zi, ps.c_str());
//printVUI(pi);
}
VUI bestPerm = get<2>(pairs[0]);
bestAP.push_back(bestPerm);
return bestAP;
}