VUI uiSeq(const unsigned int n1, const unsigned int n2, const unsigned int ns) {
VUI uis = {};
assert (n1 <= n2);
assert (0 < ns);
for (unsigned int i = n1; i <= n2; i=i+ns)
uis.push_back(i);
return uis;
}
void initScen(uint64_t sd) {
using KBase::quadUfromV;
auto rng = new PRNG(sd);
const unsigned int numA = 40;
const unsigned int numItm = 7;
const auto govCost = KMatrix::uniform(rng, 1, numItm, 25, 100); //col-vec
const double govBudget = 0.625 * sum(govCost); // cannot afford everything
const double obFactor = 0.125;
// The 'riVals' matrix shows the value to the actor (row) of each reform item (clm),
// not the utility of entire positions (which are permutations of items)
const KMatrix riVal = KMatrix::uniform(rng, numA, numItm, 10, 100);
const double pDecline = 0.8750;
vector<double> aCap = {};
for (unsigned int i = 0; i < numA; i++)
{
double ac = rng->uniform(2.0, 4.0); // [4.0, 16.0] with median at 9.0
ac = rng->uniform(17.0, 18.0)*ac*ac;
aCap.push_back(ac);
}
vector<double> prob = {};
double pj = 1.0;
printf("pDecline factor: %.3f \n", pDecline);
printf("obFactor: %.3f \n", obFactor);
// rate of decline has little effect on the results.
for (unsigned int j = 0; j < numItm; j++) {
prob.push_back(pj);
pj = pj * pDecline;
}
cout << "Computing positions ... " << endl;
vector<VUI> positions; // list of all positions
VUI pstn;
// build the first permutation: 1,2,3,...
for (unsigned int i = 0; i < numItm; i++) {
pstn.push_back(i);
}
positions.push_back(pstn);
while (next_permutation(pstn.begin(), pstn.end())) {
positions.push_back(pstn);
}
const unsigned int numPos = positions.size();
cout << "For " << numItm << " reform items there are ";
cout << numPos << " positions" << endl;
cout << "Building position utility matrix ... " << flush;
auto rpValFn = [positions, riVal, aCap, govCost, govBudget, obFactor, prob](unsigned int ai, unsigned int pj) {
VUI pstn = positions[pj];
double rvp = rawValPos(ai, pstn, riVal, aCap, govCost, govBudget, obFactor, prob);
return rvp;
};
const auto rpRawVal = KMatrix::map(rpValFn, numA, numPos);
const auto rpNormVal = KBase::rescaleRows(rpRawVal, 0.0, 1.0);
const double bigR = 0.5;
auto curve = [bigR](double v) {
return quadUfromV(v, bigR);
};
const auto rpUtil = KMatrix::map(curve, rpNormVal);
cout << "done." << endl << flush;
// This is an attempt to define a domain-independent measure of similarity,
// by looking at the difference in outcomes to actors.
// Notice that if we sort the columns by difference from #i,
// those with small differences in outcome might do it by very different
// means, so that columns from all over the matrix are placed near i.
auto diffFn = [](unsigned int i, unsigned int j, const KMatrix& uMat) {
const auto colI = KBase::vSlice(uMat, i);
const auto colJ = KBase::vSlice(uMat, j);
for (unsigned int k=0;k<colI.numR(); k++){
}
double dij = KBase::norm(colI - colJ);
return dij;
};
auto diffVUI = [&rpUtil, numPos, diffFn](unsigned int n, unsigned int nSim) {
vector<TDI> vdk = {};
for (unsigned int k = 0; k < numPos; k++) {
double dkn = diffFn(k, n, rpUtil);
auto dk = TDI(dkn, k);
vdk.push_back(dk);
}
auto tupleLess = [](TDI t1, TDI t2) {
double d1 = get<0>(t1);
double d2 = get<0>(t2);
return (d1 < d2);
};
std::sort(vdk.begin(), vdk.end(), tupleLess);
vector<TDI> sdk = {};
for (unsigned int i = 0; ((i < nSim) && (i < numPos)); i++) {
sdk.push_back(vdk[i]);
}
return sdk;
};
// The permutations with outcomes most similar to the given
// one are those which make the most minor changes
// (somewhat similar to a vector hill climbing search where the
// points in a nearby neighborhood make small changes in objective).
// So looking at a few dozen (out of thousands) might be enough to
// get significant variation to keep the search progressing.
unsigned int numClose = 50;
unsigned int rand1 = rng->uniform(0, numPos);
auto rslt1 = diffVUI(rand1, numClose);
cout << "Permutations with outcomes most similar to " << rand1 << endl;
for (unsigned int i = 0; i < rslt1.size(); i++) {
auto dp = rslt1[i];
double d = get<0>(dp);
unsigned int p = get<1>(dp);
auto posP = positions[p];
printf("%2u: %4u %.4f ", i, p, d);
KBase::printVUI(posP);
cout << endl;
}
delete rng;
rng = nullptr;
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;
}