Every order of arrival for three partners, and what each player adds

• at a quota of 9 Luxembourg is powerless exactly when the quota is even ×9
• the layer formula and the average over all 3! orders agree for A ×2
• the layer formula and the average over all 3! orders agree for B ×2
• the layer formula and the average over all 3! orders agree for C ×2
• the quota is a whole number between 1 and 120 ×2
• the weights is a list of 3 to 3 numbers ×2
• A and B are interchangeable ×1
• a division outside the core is refused by some group ×1
• a family demanding more than there is rules the core out ×1
• a game that is not convex has an arrival-order vector the core refuses ×1
• a member who can never swing a vote has no power by either count ×1
• a merger helps under majority and hurts under unanimity and under a quota short of it ×1
• a network view's game is one of its own ×1
• a rational is a whole numerator over a non-zero whole denominator ×1
• a rational is never divided by zero ×1
• a satisfied set of certificates finds splits, unless the core is a single point off the lattice ×1
• a split some coalition can beat is objected to ×1
• a stable split is one every objection to which can be answered ×1
• a whole-number seed ×1
• an even number of players from 6 to 60 ×1
• an input the model never reads gets nothing when the unknowns are filled independently ×1
• and at least one of the other rules fails one ×1
• and D adds nothing ×1
• and every corner of the core is one of them ×1
• and in 1981 more than in 1973 ×1
• and it falls at about the square-root rate over the whole sweep ×1
• and neither end gains from losing it ×1
• and satisfies the other three ×1
• and the additivity column's rule gives a different answer here ×1
• and the efficiency column's rule gives a different answer here ×1
• and the symmetry column's rule gives a different answer here ×1
• and the the null player column's rule gives a different answer here ×1
• and their heights add to it ×1
• at least one assembly drawn has power and weight ordered differently ×1
• at least one family is satisfied, so the table is separating them ×1
• averaging what each adds satisfies all four on this game ×1
• averaging what each player adds passes every condition on every game tested ×1
• below one half the line beats every split off it ×1
• between one and four assemblies ×1
• between three and eight increasing sample sizes ×1
• Bird's division is one no group refuses ×1
• Bird's payments add to the cost of the whole tree ×1
• both cheapest trees cost the same ×1
• C is not interchangeable with them, so symmetry is a real condition here ×1
• cut is read only by the linkcut view ×1
• cutting a link changes both of its ends by the same amount ×1
• donations that raised the donor's share of orders ×1
• each entry of the capacities the users need is a whole number between 1 and 200 ×1
• each entry of the split argued about, as three weights is a whole number between 0 and 100 ×1
• each entry of the weights is a whole number between 1 and 40 ×1
• each share lands on the grid the search used ×1
• every arrival-order vector shares out exactly the whole ×1
• every coalition's value is a whole number ×1
• every estimate is a share ×1
• every family in the table really is balanced ×1
• every held share below one half gives a stable set ×1
• every marked split really attains the smallest imbalance ×1
• every merger lost, gained or broke even ×1
• every order adds exactly the number of pairs, one arrival at a time ×1
• every order has exactly one pivotal member ×1
• every ordering ends with everybody in ×1
• every other split on the lattice is beaten by one of the three ×1
• every price is in the core when the sides are equal ×1
• every split hands out the whole ×1
• every split outside the core is beaten from inside it ×1
• fill is read only by the attribtable view ×1
• filled from matching houses, the unread input takes credit ×1
• fills is read only by the attrib view ×1
• graph is read only by the network and linkcut views ×1
• graphs is read only by the networks view ×1
• in 1958 Luxembourg is never pivotal ×1
• in 1973, with more members to share with, Luxembourg has power ×1
• in a convex game every arrival-order vector is a corner of the core ×1
• in the drawn case Banzhaf's share rises and the share of orders does not ×1
• mergers go both ways ×1
• model is read only by the attribution views ×1
• net is read only by the network-bill views ×1
• no coalition objects to a split none of them can beat ×1
• no coalition of the other members totals exactly one short of the quota ×1
• no group pays more under Bird's rule than its own cheapest tree would cost ×1
• no half-and-half split beats another ×1
• no other split on the table has a quieter list of complaints ×1
• no point of the line beats another ×1
• no split in the core beats another ×1
• no split survives when some balanced family over-demands ×1
• nothing both beats the split and is beaten by it ×1
• on this game the nucleolus and the average split are different points ×1
• one A and two B's block A's share 2.15, and one of each does not ×1
• one more vote on the quota and there is such a coalition ×1
• one to three networks ×1
• relaxing by less does not ×1
• relaxing by the computed amount lets a split through ×1
• short in proportion, the scarce side's share rises towards the whole pair ×1
• so their average lies in the core ×1
• some coalition holds one player and not the other ×1
• some coalition objects to every split drawn here ×1
• some donation raises the donor's normalised Banzhaf share ×1
• some family attains the maximum ×1
• some house in the data matches the known inputs ×1
• some split is individually rational ×1
• some split on the lattice pays every player at least what they earn alone ×1
• somebody can swing something, or the assembly decides nothing ×1
• the allocation uses exactly the market's goods ×1
• the average split is the average of the arrival-order vectors ×1
• the B's gain and the A is held exactly level ×1
• the balance verdict is computed for every split ×1
• the bill is drawn on a triangle for three users ×1
• the capacities the users need is a list of 2 to 5 numbers ×1
• the census finds enlargements in which an old member gains ×1
• the certificate is drawn for three players ×1
• the closed-form shares pay the whole bill ×1
• the coalitions together demand more than there is to give ×1
• the core is drawn for three players ×1
• the core of the convex game is not empty ×1
• the core, nucleolus and excess views are written for a game whose value is shared out, and this game's value is a bill ×1
• the core's corners are found for three players ×1
• the credits add up to the prediction less the starting value ×1
• the cut is one of the network's links ×1
• the denominator the splits are searched over is a whole number between 12 and 180 ×1
• the empty coalition is worth nothing ×1
• the error at the largest sample is a third of the error at the smallest ×1
• the error is a distance ×1
• the exact arithmetic stays inside the safe integer range ×1
• the exact shares add to one ×1
• the excess over a half lies between 0 and 0.45/√n ×1
• the family chosen is a whole number between 1 and 5 ×1
• the fill is one of baseline, marginal, conditional ×1
• the fills are baseline, marginal or conditional ×1
• the game is big enough that listing the orders is the point ×1
• the game is one of majority, pairs ×1
• the game is one of partnership, majority, gloves, shops, capacity, dummy, square ×1
• the game names a value for every coalition ×1
• the go-between takes the largest share ×1
• the grid divides the whole group's value evenly ×1
• the group A pays no more together than it would alone ×1
• the group AB pays no more together than it would alone ×1
• the group ABC pays no more together than it would alone ×1
• the group ABCD pays no more together than it would alone ×1
• the group ABD pays no more together than it would alone ×1
• the group AC pays no more together than it would alone ×1
• the group ACD pays no more together than it would alone ×1
• the group AD pays no more together than it would alone ×1
• the group B pays no more together than it would alone ×1
• the group BC pays no more together than it would alone ×1
• the group BCD pays no more together than it would alone ×1
• the group BD pays no more together than it would alone ×1
• the group C pays no more together than it would alone ×1
• the group CD pays no more together than it would alone ×1
• the group D pays no more together than it would alone ×1
• the held share lies on the lattice ×1
• the imbalance separates the splits, so the condition bites ×1
• the kernel is drawn for three players ×1
• the lattice holds every value exactly ×1
• the layer formula and the average over all 4! orders agree for D ×1
• the layers stack up to the largest requirement ×1
• the least core is drawn for three players ×1
• the marginal contributions along one ordering add up to the whole ×1
• the marginal view is drawn for three players ×1
• the marginal view is written for a game whose value is shared out ×1
• the model is one of proxy, and ×1
• the network is one of line3, triangle, vee, star4, bridge ×1
• the network is one of remote, far, tie ×1
• the network's whole earning is shared out ×1
• the nucleolus survives every objection exactly when some split does ×1
• the number of users is a whole number between 4 and 11 ×1
• the objection is drawn for three players ×1
• the other tree's Bird division is in the core too ×1
• the others fail ×1
• the pairwise surpluses are drawn for three players ×1
• the picture is symmetric between B and C ×1
• the power shares add to one ×1
• the proportional rule needs somebody to be worth something alone ×1
• the proposed split is beaten ×1
• the proposed split shares out the three pairs ×1
• the quota is more than half the weight and no more than all of it ×1
• the rarer input of the product takes the larger share ×1
• the requirements are given smallest first ×1
• the resolution of the exhaustive sweep is a whole number between 12 and 120 ×1
• the resolution of the relaxed sweep is a whole number between 12 and 120 ×1
• the resolution of the sweep the verdict is checked against is a whole number between 12 and 120 ×1
• the resolution the proposals are searched over is a whole number between 8 and 48 ×1
• the rule in the additivity column fails additive ×1
• the rule in the efficiency column fails efficient ×1
• the rule in the symmetry column fails symmetric ×1
• the rule in the the null player column fails null player ×1
• the scarce side takes everything ×1
• the scarce side's share falls as the market grows ×1
• the search finds no balanced family of at most three coalitions outside the table ×1
• the search is written for three players ×1
• the second game names a whole value for each of the eight coalitions of three, starting at nothing ×1
• the seed is a whole number between 0 and 10000 ×1
• the shares add to what the whole group is worth ×1
• the shares add up to what the whole group is worth ×1
• the split argued about, as three weights is a list of 3 to 3 numbers ×1
• the split hands out the whole ×1
• the split is three shares adding to one ×1
• the split lies on the lattice ×1
• the splits achieving the minimum are one point to within a grid step ×1
• the splits give different surpluses, so the table is comparing them ×1
• the subset formula and the average over orders agree ×1
• the sweep and the balancedness condition agree about whether any split survives ×1
• the symmetric set and the low line are stable ×1
• the table is drawn for three players ×1
• the test is drawn for three players ×1
• the three lefts and three of the rights earn more alone than they are paid ×1
• the users do not all need the same thing, or there is nothing to divide unevenly ×1
• the view is one of axioms, core, nucleolus, excess, unique, power, sample, layers, balanced, certificate, leastcore, surplus, kernel, counter, attrib, attribtable, attribdata, network, networks, linkcut, marginals, convexity, mst, mstcore, msttable, mstbig, stabledom, stablesym, stablediscrim, stablecheck, stableconvex, eec, parity, quotasweep, newmembers, merge, donate, glovestep, glovepath, glovereplica, gloveblock, gloveequal, repbox, repshrink, reprate, repwho, repcoalition, repequal ×1
• the weights are not all nought ×1
• the weights are positive ×1
• the whole group is worth a whole number ×1
• the worst-treated A and B both prefer splitting their joint endowment evenly ×1
• there is more than one layer, or the figure has nothing to show ×1
• two games on the same number of players ×1
• two hundred lefts against three hundred rights take nearly everything ×1
• two to four games this family knows ×1
• users is read only by the large network view ×1
• what all four players are worth together is a whole number between 4 and 40 ×1
• when a stable split exists, every balanced split is one ×1
• width times r settles from twenty replicas ×1
• with equal sides the average over orders splits each pair evenly ×1
• with every input known the value is the prediction itself ×1
• with fewer links than some of the others ×1

The whole library · What the figures prove