// calculate the [option,1] column vector of option-probabilities.
// w is a [1,actor] row-vector of actor strengths, u is [act,option] utilities.
// This assumes scalar capabilities of actors (w), so that the voting strength
// is a direct function of difference in utilities.Therefore, we can use
// Model::vProb(VotingRule vr, const KMatrix & w, const KMatrix & u)
KMatrix Model::scalarPCE(unsigned int numAct, unsigned int numOpt, const KMatrix & w, const KMatrix & u,
VotingRule vr, VPModel vpm, PCEModel pcem, ReportingLevel rl) {
// auto pv = Model::vProb(vr, vpm, w, u);
// auto p = Model::probCE(pcem, pv);
auto vfn = [vr, &w, &u](unsigned int k, unsigned int i, unsigned int j) {
double vkij = vote(vr, w(0, k), u(k, i), u(k, j));
return vkij;
};
const auto c = coalitions(vfn, numAct, numOpt); // c(i,j) = strength of coaltion for i against j
const auto pv2 = Model::probCE2(pcem, vpm, c);
const auto p = get<0>(pv2); //column
const auto pv = get<1>(pv2); // square
if (ReportingLevel::Low < rl) {
printf("Num actors: %i \n", numAct);
printf("Num options: %i \n", numOpt);
if ((numAct <= 20) && (numOpt <= 20)) {
cout << "Actor strengths: " << endl;
w.mPrintf(" %6.2f ");
cout << endl << flush;
cout << "Voting rule: " << vr << endl;
// printf(" aka %s \n", KBase::vrName(vr).c_str());
cout << flush;
cout << "Utility to actors of options: " << endl;
u.mPrintf(" %+8.3f ");
cout << endl << flush;
cout << "Coalition strengths of (i:j): " << endl;
c.mPrintf(" %8.3f ");
cout << endl;
cout << "Probability Opt_i > Opt_j" << endl;
pv.mPrintf(" %.4f ");
cout << "Probability Opt_i" << endl;
p.mPrintf(" %.4f ");
}
cout << "Found stable PCE distribution" << endl << flush;
}
return p;
}
RPState* RPState::doSUSN(ReportingLevel rl) const {
RPState* s2 = nullptr;
const unsigned int numA = model->numAct;
assert(numA == rpMod->actrs.size());
const unsigned int numU = uIndices.size();
assert ((0 < numU) && (numU <= numA));
assert (numA == eIndices.size());
// TODO: filter out essentially-duplicate positions
//printf("RPState::doSUSN: numA %i \n", numA);
//printf("RPState::doSUSN: numP %i \n", numP);
//cout << endl << flush;
const KMatrix u = aUtil[0]; // all have same beliefs in this demo
auto vpm = VPModel::Linear;
const unsigned int numP = pstns.size();
// Given the utility matrix, uMat, calculate the expected utility to each actor,
// as a column-vector. Again, this is from the perspective of whoever developed uMat.
auto euMat = [rl, numA, numP, vpm, this](const KMatrix & uMat) {
// BTW, be sure to lambda-bind uMat *after* it is modified.
assert(uMat.numR() == numA); // must include all actors
assert(uMat.numC() <= numP); // might have dropped some duplicates
auto uRng = [uMat](unsigned int i, unsigned int j) {
if ((uMat(i, j) < 0.0) || (1.0 < uMat(i, j))) {
printf("%f %i %i \n", uMat(i, j), i, j);
cout << flush;
cout << flush;
}
assert(0.0 <= uMat(i, j));
assert(uMat(i, j) <= 1.0);
return;
};
KMatrix::mapV(uRng, uMat.numR(), uMat.numC());
// vote_k ( i : j )
auto vkij = [this, uMat](unsigned int k, unsigned int i, unsigned int j) {
auto ak = (RPActor*)(rpMod->actrs[k]);
auto v_kij = Model::vote(ak->vr, ak->sCap, uMat(k, i), uMat(k, j));
return v_kij;
};
// the following uses exactly the values in the given euMat,
// which may or may not be square
const KMatrix c = Model::coalitions(vkij, uMat.numR(), uMat.numC());
const KMatrix pv = Model::vProb(vpm, c); // square
const KMatrix p = Model::probCE(PCEModel::ConditionalPCM, pv); // column
const KMatrix eu = uMat*p; // column
assert(numA == eu.numR());
assert(1 == eu.numC());
auto euRng = [eu](unsigned int i, unsigned int j) {
// due to round-off error, we must have a tolerance factor
const double tol = 1E-10;
const double euij = eu(i, j);
assert(0.0 <= euij+tol);
assert(euij <= 1.0+tol);
return;
};
KMatrix::mapV(euRng, eu.numR(), eu.numC());
if (ReportingLevel::Low < rl) {
printf("Util matrix is %i x %i \n", uMat.numR(), uMat.numC());
cout << "Assessing EU from util matrix: " << endl;
uMat.mPrintf(" %.6f ");
cout << endl << flush;
cout << "Coalition strength matrix" << endl;
c.mPrintf(" %12.6f ");
cout << endl << flush;
cout << "Probability Opt_i > Opt_j" << endl;
pv.mPrintf(" %.6f ");
cout << endl << flush;
cout << "Probability Opt_i" << endl;
p.mPrintf(" %.6f ");
cout << endl << flush;
cout << "Expected utility to actors: " << endl;
eu.mPrintf(" %.6f ");
cout << endl << flush;
}
return eu;
};
// end of euMat
auto euState = euMat(u);
cout << "Actor expected utilities: ";
KBase::trans(euState).mPrintf("%6.4f, ");
cout << endl << flush;
if (ReportingLevel::Low < rl) {
printf("--------------------------------------- \n");
printf("Assessing utility of actual state to all actors \n");
for (unsigned int h = 0; h < numA; h++) {
cout << "not available" << endl;
}
cout << endl << flush;
printf("Out of %u positions, %u were unique: ", numA, numU);
cout << flush;
for (auto i : uIndices) {
printf("%2i ", i);
}
cout << endl;
cout << flush;
}
auto uufn = [u, this](unsigned int i, unsigned int j1) {
return u(i, uIndices[j1]);
};
auto uUnique = KMatrix::map(uufn, numA, numU);
// Get expected-utility vector, one entry for each actor, in the current state.
const KMatrix eu0 = euMat(uUnique); // 'u' with duplicates, 'uUnique' without duplicates
s2 = new RPState(model);
//s2->pstns = vector<KBase::Position*>();
for (unsigned int h = 0; h < numA; h++) {
s2->pstns.push_back(nullptr);
}
// TODO: clean up the nesting of lambda-functions.
// need to create a hypothetical state and run setOneAUtil(h,Silent) on it
//
// The newPosFn does a GA optimization to find the best next position for actor h,
// and stores it in s2. To do that, it defines three functions for evaluation, neighbors, and show:
// efn, nfn, and sfn.
auto newPosFn = [this, rl, euMat, u, eu0, s2](const unsigned int h) {
s2->pstns[h] = nullptr;
auto ph = ((const MtchPstn *)(pstns[h]));
// Evaluate h's estimate of the expected utility, to h, of
// advocating position mp. To do this, build a hypothetical utility matrix representing
// h's estimates of the direct utilities to all other actors of h adopting this
// Position. Do that by modifying the h-column of h's matrix.
// Then compute the expected probability distribution, over h's hypothetical position
// and everyone else's actual position. Finally, compute the expected utility to
// each actor, given that distribution, and pick out the value for h's expected utility.
// That is the expected value to h of adopting the position.
auto efn = [this, euMat, rl, u, h](const MtchPstn & mph) {
// This correctly handles duplicated/unique options
// We modify the given euMat so that the h-column
// corresponds to the given mph, but we need to prune duplicates as well.
// This entails some type-juggling.
const KMatrix uh0 = aUtil[h];
assert(KBase::maxAbs(u - uh0) < 1E-10); // all have same beliefs in this demo
if (mph.match.size() != rpMod->numItm) {
cout << mph.match.size() << endl << flush;
cout << rpMod->numItm << endl << flush;
cout << flush << flush;
}
assert(mph.match.size() == rpMod->numItm);
auto uh = uh0;
for (unsigned int i = 0; i < rpMod->numAct; i++) {
auto ai = (RPActor*)(rpMod->actrs[i]);
double uih = ai->posUtil(&mph);
uh(i, h) = uih; // utility to actor i of this hypothetical position by h
}
// 'uh' now has the correct h-column. Now we need to see how many options
// are unique in the hypothetical state, and keep only those columns.
// This entails juggling back and forth between the all current positions
// and the one hypothetical position (mph at h).
// Thus, the next call to euMat will consider only unique options.
auto equivHNdx = [this, h, mph](const unsigned int i, const unsigned int j) {
// this little function takes care of the different types needed to compare
// dynamic pointers to positions (all but h) with a constant position (h itself).
// In other words, the comparisons for index 'h' use the hypothetical mph, not pstns[h]
bool rslt = false;
auto mpi = ((const MtchPstn *)(pstns[i]));
auto mpj = ((const MtchPstn *)(pstns[j]));
assert(mpi != nullptr);
assert(mpj != nullptr);
if (i == j) {
rslt = true; // Pi == Pj, always
}
else if (h == i) {
rslt = (mph == (*mpj));
}
else if (h == j) {
rslt = ((*mpi) == mph);
}
else {
rslt = ((*mpi) == (*mpj));
}
return rslt;
};
auto ns = KBase::uiSeq(0, model->numAct - 1);
const VUI uNdx = get<0>(KBase::ueIndices<unsigned int>(ns, equivHNdx));
const unsigned int numU = uNdx.size();
auto hypUtil = KMatrix(rpMod->numAct, numU);
// we need now to go through 'uh', copying column J the first time
// the J-th position is determined to be equivalent to something in the unique list
for (unsigned int i = 0; i < rpMod->numAct; i++) {
for (unsigned int j1 = 0; j1 < numU; j1++) {
unsigned int j2 = uNdx[j1];
hypUtil(i, j1) = uh(i, j2); // hypothetical utility in column h
}
}
if (false) {
cout << "constructed hypUtil matrix:" << endl << flush;
hypUtil.mPrintf(" %8.2f ");
cout << endl << flush;
}
if (ReportingLevel::Low < rl) {
printf("--------------------------------------- \n");
printf("Assessing utility to %2i of hypo-pos: ", h);
printPerm(mph.match);
cout << endl << flush;
printf("Hypo-util minus base util: \n");
(uh - uh0).mPrintf(" %+.4E ");
cout << endl << flush;
}
const KMatrix eu = euMat(hypUtil); // uh or hypUtil
// BUG: If we use 'uh' here, it passes the (0 <= delta-EU) test, because
// both hypothetical and actual are then calculated without dropping duplicates.
// If we use 'hypUtil' here, it sometimes gets (delta-EU < 0), because
// the hypothetical drops duplicates but the actual (computed elsewhere) does not.
// FIX: fix the 'elsewhere'
const double euh = eu(h, 0);
assert(0 < euh);
//cout << euh << endl << flush;
//printPerm(mp.match);
//cout << endl << flush;
//cout << flush;
return euh;
}; // end of efn
/*
// I do not actually use prevMP, but it is still an example for std::set
auto prevMP = [](const MtchPstn & mp1, const MtchPstn & mp2) {
bool r = std::lexicographical_compare(
mp1.match.begin(), mp1.match.end(),
mp2.match.begin(), mp2.match.end());
return r;
};
std::set<MtchPstn, bool(*)(const MtchPstn &, const MtchPstn &)> mpSet(prevMP);
*/
// return vector of neighboring 1-permutations
auto nfn = [](const MtchPstn & mp0) {
const unsigned int numI = mp0.match.size();
auto mpVec = vector <MtchPstn>();
mpVec.push_back(MtchPstn(mp0));
// one-permutations
for (unsigned int i = 0; i < numI; i++) {
for (unsigned int j = i + 1; j < numI; j++) {
unsigned int ei = mp0.match[i];
unsigned int ej = mp0.match[j];
auto mij = MtchPstn(mp0);
mij.match[i] = ej;
mij.match[j] = ei;
mpVec.push_back(mij);
}
}
// two-permutations
for (unsigned int i = 0; i < numI; i++) {
for (unsigned int j = i + 1; j < numI; j++) {
for (unsigned int k = j + 1; k < numI; k++) {
unsigned int ei = mp0.match[i];
unsigned int ej = mp0.match[j];
unsigned int ek = mp0.match[k];
auto mjki = MtchPstn(mp0);
mjki.match[i] = ej;
mjki.match[j] = ek;
mjki.match[k] = ei;
mpVec.push_back(mjki);
auto mkij = MtchPstn(mp0);
mkij.match[i] = ek;
mkij.match[j] = ei;
mkij.match[k] = ej;
mpVec.push_back(mkij);
}
}
}
//unsigned int mvs = mpVec.size() ;
//cout << mvs << endl << flush;
//cout << flush;
return mpVec;
}; // end of nfn
// show some representation of this position on cout
auto sfn = [](const MtchPstn & mp0) {
printPerm(mp0.match);
return;
};
auto ghc = new KBase::GHCSearch<MtchPstn>();
ghc->eval = efn;
ghc->nghbrs = nfn;
ghc->show = sfn;
auto rslt = ghc->run(*ph, // start from h's current positions
ReportingLevel::Silent,
100, // iter max
3, 0.001); // stable-max, stable-tol
if (ReportingLevel::Low < rl) {
printf("---------------------------------------- \n");
printf("Search for best next-position of actor %2i \n", h);
//printf("Search for best next-position of actor %2i starting from ", h);
//trans(*aPos).printf(" %+.6f ");
cout << flush;
}
double vBest = get<0>(rslt);
MtchPstn pBest = get<1>(rslt);
unsigned int iterN = get<2>(rslt);
unsigned int stblN = get<3>(rslt);
delete ghc;
ghc = nullptr;
if (ReportingLevel::Medium < rl) {
printf("Iter: %u Stable: %u \n", iterN, stblN);
printf("Best value for %2i: %+.6f \n", h, vBest);
cout << "Best position: " << endl;
cout << "numCat: " << pBest.numCat << endl;
cout << "numItm: " << pBest.numItm << endl;
cout << "perm: ";
printPerm(pBest.match);
cout << endl << flush;
}
MtchPstn * posBest = new MtchPstn(pBest);
s2->pstns[h] = posBest;
// no need for mutex, as s2->pstns is the only shared var,
// and each h is different.
double du = vBest - eu0(h, 0); // (hypothetical, future) - (actual, current)
if (ReportingLevel::Low < rl) {
printf("EU improvement for %2i of %+.4E \n", h, du);
}
//printf(" vBest = %+.6f \n", vBest);
//printf(" eu0(%i, 0) for %i = %+.6f \n", h, h, eu0(h,0));
//cout << endl << flush;
// Logically, du should always be non-negative, as GHC never returns a worse value than the starting point.
// However, actors plan on the assumption that all others do not change - yet they do.
const double eps = 0.05; // 0.025; // enough to avoid problems with round-off error
assert(-eps <= du);
return;
}; // end of newPosFn
const bool par = true;
auto ts = vector<thread>();
// Each actor, h, finds the position which maximizes their EU in this situation.
for (unsigned int h = 0; h < numA; h++) {
if (par) { // launch all, concurrent
ts.push_back(thread([newPosFn, h]() {
newPosFn(h);
return;
}));
}
else { // do each, sequential
newPosFn(h);
}
}
if (par) { // now join them all before continuing
for (auto& t : ts) {
t.join();
}
}
assert(nullptr != s2);
assert(numP == s2->pstns.size());
assert(numA == s2->model->numAct);
for (auto p : s2->pstns) {
assert(nullptr != p);
}
s2->setUENdx();
return s2;
}
// 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;
}