{"text_format":"3","workbook":"xlsx","n_sheets":1,"sheets":["DATA"],"not_rendered":{"macros":1,"defined_names":23},"read":"whole","date_system":"1900"}

{"sheet":"DATA","index":0,"n_rows":85,"n_cols":8,"rows_kept":85,"merged":[[0,0,0,5],[2,0,2,5],[4,0,4,5],[5,0,5,5],[7,2,7,3],[9,0,9,5],[11,2,11,3]]}
["WEIGHTED VOTING SYSTEM CALCULATOR"]
[]
["Computes Voting Power Indexes"]
[]
["Robert A. Agnew, raagnew1@gmail.com"]
["www.raagnew.com"]
[]
[null,null,"Inputs"]
[]
["Click  View > Macros > View Macros > Run  in Excel 2016"]
[]
["# of Players",51,"Root Mean Square Distance",null,{"$f":"SQRT(SUM(G16:G66))","v":{"v":0.011649886748074278,"d":"1.16499%"}},{"$f":"SQRT(SUM(H16:H66))","v":{"v":0.008784854066054937,"d":"0.8784854%"}}]
["Quota",270,null,null,"Banzhaf","Shapley"]
[null,"2010 Census","Voting",null,"Coleman","Shubik","Squared","Squared"]
["Player","Votes","Index","Swings","Index","Index","Deviations","Deviations"]
["California",55,{"$f":"B16/B$67","v":{"v":0.10223048327137546,"d":"10.223%"}},530464653682739,{"$f":"D16/D$67","v":{"v":0.11360822958596903,"d":"11.361%"}},{"v":0.11029686127090108,"d":"11.030%"},{"$f":"(C16-E16)^2","v":1.2945311119924751E-4},{"$f":"(C16-F16)^2","v":6.5066454031230856E-5}]
["Texas",38,{"v":0.07063197026022305,"d":"7.063%"},336488186697933,{"$f":"D17/D$67","v":{"v":0.07206479621582577,"d":"7.206%"}},{"v":0.07322277339987077,"d":"7.322%"},2.0529902190488495E-6,6.7122609084084454E-6]
["New York",29,{"v":0.05390334572490706,"d":"5.390%"},252173735474113,{"v":0.05400739038199686,"d":"5.401%"},{"v":0.054833851214937765,"d":"5.483%"},1.0825290668933408E-8,8.658404669772762E-7]
["Florida",29,{"v":0.05390334572490706,"d":"5.390%"},252173735474113,{"v":0.05400739038199686,"d":"5.401%"},{"v":0.054833851214937765,"d":"5.483%"},1.0825290668933408E-8,8.658404669772762E-7]
["Illinois",20,{"v":0.03717472118959108,"d":"3.717%"},171659645743663,{"v":0.0367638980446677,"d":"3.676%"},{"v":0.037149583970104365,"d":"3.715%"},1.6877565640473362E-7,6.318798035232838e-10]
["Pennsylvania",20,{"v":0.03717472118959108,"d":"3.717%"},171659645743663,{"v":0.0367638980446677,"d":"3.676%"},{"v":0.037149583970104365,"d":"3.715%"},1.6877565640473362E-7,6.318798035232838e-10]
["Ohio",18,{"v":0.03345724907063197,"d":"3.346%"},154159781773031,{"v":0.033015997878471426,"d":"3.302%"},{"v":0.03330711472131342,"d":"3.331%"},1.9470261458309877E-7,2.2540322845304234E-8]
["Michigan",16,{"v":0.02973977695167286,"d":"2.974%"},136768683131125,{"v":0.02929139169869085,"d":"2.929%"},{"v":0.02949472845371744,"d":"2.949%"},2.0104933509174056E-7,6.0048766350208031E-8]
["Georgia",16,{"v":0.02973977695167286,"d":"2.974%"},136768683131125,{"v":0.02929139169869085,"d":"2.929%"},{"v":0.02949472845371744,"d":"2.949%"},2.0104933509174056E-7,6.0048766350208031E-8]
["North Carolina",15,{"v":0.027881040892193308,"d":"2.788%"},128109515949679,{"v":0.02743688047660786,"d":"2.744%"},{"v":0.027599593960101414,"d":"2.760%"},1.97278474773037E-7,7.9212375583939424E-8]
["New Jersey",14,{"v":0.026022304832713755,"d":"2.602%"},119472352338831,{"v":0.025587081701778154,"d":"2.559%"},{"v":0.02571171731093029,"d":"2.571%"},1.8941917370138738E-7,9.6464608687594167E-8]
["Virginia",13,{"v":0.024163568773234202,"d":"2.416%"},110855556137941,{"v":0.02374164496195024,"d":"2.374%"},{"v":0.023831015230066206,"d":"2.383%"},1.7801970252838376E-7,1.1059185907358819E-7]
["Washington",12,{"v":0.022304832713754646,"d":"2.230%"},102257528272361,{"v":0.0219002277874827,"d":"2.190%"},{"v":0.021957406225923237,"d":"2.196%"},1.63705146363528e-07,1.2070516444686791E-7]
["Massachusetts",11,{"v":0.020446096654275093,"d":"2.045%"},93676703259355,{"v":0.020062494903026175,"d":"2.006%"},{"v":0.020090810582924713,"d":"2.009%"},1.4715030356123678E-7,1.2622819249558748E-7]
["Indiana",11,{"v":0.020446096654275093,"d":"2.045%"},93676703259355,{"v":0.020062494903026175,"d":"2.006%"},{"v":0.020090810582924713,"d":"2.009%"},1.4715030356123678E-7,1.2622819249558748E-7]
["Arizona",11,{"v":0.020446096654275093,"d":"2.045%"},93676703259355,{"v":0.020062494903026175,"d":"2.006%"},{"v":0.020090810582924713,"d":"2.009%"},1.4715030356123678E-7,1.2622819249558748E-7]
["Tennessee",11,{"v":0.020446096654275093,"d":"2.045%"},93676703259355,{"v":0.020062494903026175,"d":"2.006%"},{"v":0.020090810582924713,"d":"2.009%"},1.4715030356123678E-7,1.2622819249558748E-7]
["Missouri",10,{"v":0.01858736059479554,"d":"1.859%"},85111546023493,{"v":0.018228117545484628,"d":"1.823%"},{"v":0.018231150417132327,"d":"1.823%"},1.2905556847820212E-7,1.2688569067085788E-7]
["Maryland",10,{"v":0.01858736059479554,"d":"1.859%"},85111546023493,{"v":0.018228117545484628,"d":"1.823%"},{"v":0.018231150417132327,"d":"1.823%"},1.2905556847820212E-7,1.2688569067085788E-7]
["Wisconsin",10,{"v":0.01858736059479554,"d":"1.859%"},85111546023493,{"v":0.018228117545484628,"d":"1.823%"},{"v":0.018231150417132327,"d":"1.823%"},1.2905556847820212E-7,1.2688569067085788E-7]
["Minnesota",10,{"v":0.01858736059479554,"d":"1.859%"},85111546023493,{"v":0.018228117545484628,"d":"1.823%"},{"v":0.018231150417132327,"d":"1.823%"},1.2905556847820212E-7,1.2688569067085788E-7]
["Colorado",9,{"v":0.016728624535315983,"d":"1.673%"},76560548827465,{"v":0.01639677280669579,"d":"1.640%"},{"v":0.016378349507903837,"d":"1.638%"},1.1012556978821023E-7,1.2269259482857968E-7]
["Alabama",9,{"v":0.016728624535315983,"d":"1.673%"},76560548827465,{"v":0.01639677280669579,"d":"1.640%"},{"v":0.016378349507903837,"d":"1.638%"},1.1012556978821023E-7,1.2269259482857968E-7]
["South Carolina",9,{"v":0.016728624535315983,"d":"1.673%"},76560548827465,{"v":0.01639677280669579,"d":"1.640%"},{"v":0.016378349507903837,"d":"1.638%"},1.1012556978821023E-7,1.2269259482857968E-7]
["Louisiana",8,{"v":0.01486988847583643,"d":"1.487%"},68022228399715,{"v":0.014568143018264037,"d":"1.457%"},{"v":0.014532333311720767,"d":"1.453%"},9.1050321165573432E-8,1.1394348882115257E-7]
["Kentucky",8,{"v":0.01486988847583643,"d":"1.487%"},68022228399715,{"v":0.014568143018264037,"d":"1.457%"},{"v":0.014532333311720767,"d":"1.453%"},9.1050321165573432E-8,1.1394348882115257E-7]
["Oregon",7,{"v":0.013011152416356878,"d":"1.301%"},59495123097629,{"v":0.01274191514400776,"d":"1.274%"},{"v":0.01269302877214146,"d":"1.269%"},7.2488708821992874E-8,1.0120265300889731E-7]
["Oklahoma",7,{"v":0.013011152416356878,"d":"1.301%"},59495123097629,{"v":0.01274191514400776,"d":"1.274%"},{"v":0.01269302877214146,"d":"1.269%"},7.2488708821992874E-8,1.0120265300889731E-7]
["Connecticut",7,{"v":0.013011152416356878,"d":"1.301%"},59495123097629,{"v":0.01274191514400776,"d":"1.274%"},{"v":0.01269302877214146,"d":"1.269%"},7.2488708821992874E-8,1.0120265300889731E-7]
["Iowa",6,{"v":0.011152416356877323,"d":"1.115%"},50977790391193,{"v":0.010917780241040991,"d":"1.092%"},{"v":0.01086036444431358,"d":"1.086%"},5.5054106854760474E-8,8.529431963214024E-8]
["Mississippi",6,{"v":0.011152416356877323,"d":"1.115%"},50977790391193,{"v":0.010917780241040991,"d":"1.092%"},{"v":0.01086036444431358,"d":"1.086%"},5.5054106854760474E-8,8.529431963214024E-8]
["Arkansas",6,{"v":0.011152416356877323,"d":"1.115%"},50977790391193,{"v":0.010917780241040991,"d":"1.092%"},{"v":0.01086036444431358,"d":"1.086%"},5.5054106854760474E-8,8.529431963214024E-8]
["Kansas",6,{"$f":"B48/B$67","v":{"v":0.011152416356877323,"d":"1.115%"}},50977790391193,{"v":0.010917780241040991,"d":"1.092%"},{"v":0.01086036444431358,"d":"1.086%"},{"$f":"(C48-E48)^2","v":5.5054106854760474E-8},{"$f":"(C48-F48)^2","v":8.529431963214024E-8}]
["Utah",6,{"v":0.011152416356877323,"d":"1.115%"},50977790391193,{"v":0.010917780241040991,"d":"1.092%"},{"v":0.01086036444431358,"d":"1.086%"},5.5054106854760474E-8,8.529431963214024E-8]
["Nevada",6,{"v":0.011152416356877323,"d":"1.115%"},50977790391193,{"v":0.010917780241040991,"d":"1.092%"},{"v":0.01086036444431358,"d":"1.086%"},5.5054106854760474E-8,8.529431963214024E-8]
["New Mexico",5,{"v":0.00929368029739777,"d":"0.929%"},42468804166739,{"v":0.009095432882323708,"d":"0.910%"},{"v":9.034270342216098E-3,"d":"0.903%"},3.9302037583547539E-8,6.729352484735707E-8]
["West Virginia",5,{"v":0.00929368029739777,"d":"0.929%"},42468804166739,{"v":0.009095432882323708,"d":"0.910%"},{"v":9.034270342216098E-3,"d":"0.903%"},3.9302037583547539E-8,6.729352484735707E-8]
["Nebraska",5,{"v":0.00929368029739777,"d":"0.929%"},42468804166739,{"v":0.009095432882323708,"d":"0.910%"},{"v":9.034270342216098E-3,"d":"0.903%"},3.9302037583547539E-8,6.729352484735707E-8]
["Idaho",4,{"v":0.007434944237918215,"d":"0.743%"},33966752265447,{"v":0.007274570629489244,"d":"0.727%"},{"v":0.007214677842204031,"d":"0.721%"},2.571969428052904E-8,4.8517285080917433E-8]
["Hawaii",4,{"v":0.007434944237918215,"d":"0.743%"},33966752265447,{"v":0.007274570629489244,"d":"0.727%"},{"v":0.007214677842204031,"d":"0.721%"},2.571969428052904E-8,4.8517285080917433E-8]
["Maine",4,{"v":0.007434944237918215,"d":"0.743%"},33966752265447,{"v":0.007274570629489244,"d":"0.727%"},{"v":0.007214677842204031,"d":"0.721%"},2.571969428052904E-8,4.8517285080917433E-8]
["New Hampshire",4,{"v":0.007434944237918215,"d":"0.743%"},33966752265447,{"v":0.007274570629489244,"d":"0.727%"},{"v":0.007214677842204031,"d":"0.721%"},2.571969428052904E-8,4.8517285080917433E-8]
["Rhode Island",4,{"v":0.007434944237918215,"d":"0.743%"},33966752265447,{"v":0.007274570629489244,"d":"0.727%"},{"v":0.007214677842204031,"d":"0.721%"},2.571969428052904E-8,4.8517285080917433E-8]
["Montana",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["Delaware",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["South Dakota",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["Alaska",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["North Dakota",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["Vermont",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["District of Columbia",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["Wyoming",3,{"v":5.5762081784386614E-3,"d":"0.558%"},25470234122519,{"v":5.454893527232346E-3,"d":"0.545%"},{"v":5.401519779502391E-3,"d":"0.540%"},1.4717244597309963E-8,3.0516036722917559E-8]
["Total",{"$f":"SUM(B16:B66)","v":538},{"$f":"SUM(C16:C66)","v":{"v":0.9999999999999998,"d":"100%"}},{"$f":"SUM(D16:D66)","v":{"v":4669244962411183,"d":"4669244962411180"}},{"$f":"SUM(E16:E66)","v":{"v":0.9999999999999999,"d":"100%"}},{"$f":"SUM(F16:F66)","v":{"v":1.0000000000000004,"d":"100%"}}]
[]
["NOTE"]
["Calculator has been updated for 2010 Census and associated U.S. House apportionment."]
["Spreadsheet runs in tandem with macro Calc.  "]
["Solves Electoral College weighted voting system in less than 30 seconds on a modern PC. "]
["Change quota and click  View > Macros > View Macros > Run  in Excel 2016."]
["Root Mean Square Distance is usual L2 norm, the square root of what Tannenbaum calls \"faithfulness.\""]
["In Mathematica Journal, Vol 7, Issue 1, Winter 1997, pp. 58-63, Tannenbaum shows that Banzhaf "]
["Root Mean Square Distance is minimized at a quota of 315 using 1990 census data.  That number is now 316"]
["although it has no practical meaning since such a hurdle would never be implemented, because it would"]
["routinely throw presidential elections into the House.  Moreover, the Electoral College is clearly an artifact that"]
["needs to be replaced by direct presidential elections, but this would require unlikely changes to the U.S. Constitution.   "]
["Still, this treatment is interesting because it brings in game-theoretic power metrics which go beyond simple vote counts.   "]
[]
["Smaller weighted voting systems can be solved efficiently by changing the number of players and"]
["deleting unused cells (not rows), e.g., solve {12; 6,5,4,3,2,1} by entering 6 in B12, 12 in B13, 6,5,4,3,2,1 in "]
["B16:B21, deleting A22:F66 (again cells, not rows), solving, and saving as new file.  System with more than 51 players "]
["and/or vote total exceeding 1,000 requires editing of worksheet (including range names) and dimensions in macro."]