2b:null 2c:["$","title",null,{"children":"Monte Carlo Introduction: Comparing Voting Methods | Ron Smith | Observable"}] 31:[] 2f:{"id":"c2a6561d7e640bca","slug":"monte-carlo-introduction-simulated-elections","title":"Monte Carlo Introduction: Comparing Voting Methods","thumbnail":"553b659cd0b4ed029b72e25b1c7a6bf0c6e83cc13e19bc9fe017e71f66b99090","access_level":"public","create_time":"$D2019-03-08T16:11:59.421Z","update_time":"$D2019-03-18T18:54:03.992Z","view_time":null,"first_public_time":"$D2019-03-09T01:18:33.967Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"8dab63897b6adf13","login":"ronzor","name":"Ron Smith","avatar_url":"https://avatars-next.observableusercontent.com/72c20176307cf53407d67a22afcc4d7d49bbdd419afc85de1cf01fe8aa2e320f","tier":"starter_2024"},"version":568,"publish_version":568,"role":null,"authored":false,"authors":[{"type":"individual","id":"a5eeba816274b983","login":"ronzor","name":"Ron 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webpage`}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":448,"value":"md `--- ---\n# Simulated results`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":454,"value":"md `### **First-past-the-post**: ${html`${fWinnerName}`} wins with ${(fWinner[0]/Nvoters*100).toFixed(1) + '%'} of the vote (${fWinner[0]} of ${Nvoters})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":457,"value":"md `### **Instant-runoff**: ${html`${iWinnerName}`} wins with ${(iWinner[0]/Nvoters*100).toFixed(1) + '%'} of the vote (${iWinner[0]} of ${Nvoters})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":437,"value":"viewof IRVround = slider({\n min: 0, \n max: Ncandidates-2, \n step: 1, \n value: 0, \n title: md `Show Instant-runoff round`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":12,"value":"{\n const sz=300;\n let msa = MakeStandardAxes(0,1,\"middle\",0,1,\"middle\",sz,sz,{top:40,bottom:40,right:40,left:40}, -1);\n let svg = msa[0],X=msa[1],Y=msa[2];\n \n // Determine who is still in the race\n let status = getIRVStatus(IRVround);\n // Plot candidates still in the race\n for (let n=0;nbeta distributions`}, one for the left-right direction, and one for the up-down direction (_if you read the code, it might seem like I named the variables opposite of what the slider bar titles say... there is a reason for this!_)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":532,"value":"viewof Vleft = slider({\n min: 0, \n max: 5, \n step: 0.02, \n value: 1, \n title: md `Voters' \"right\" tendency`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":543,"value":"viewof Vright = slider({\n min: 0, \n max: 5, \n step: 0.02, \n value: 1, \n title: md `Voters' \"left\" tendency`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":552,"value":"viewof Vdown = slider({\n min: 0, \n max: 5, \n step: 0.02, \n value: 1, \n title: md `Voters' \"up\" tendency`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":549,"value":"viewof Vup = slider({\n min: 0, \n max: 5, \n step: 0.02, \n value: 1, \n title: md `Voters' \"down\" tendency`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":217,"value":"md `--- ---\n*Current candidate and voter positions*`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":93,"value":"candidatePositions = getCandidatePositions(Ncandidates)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":103,"value":"voterPositions = getVoterPositions();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":324,"value":"fWinner = getFPTPWinner();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":359,"value":"iWinner = getIRVWinner();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":221,"value":"md`--- ---\n*Distance from each voter to each candidate and functions to count votes*`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":10,"value":"function getCandidatePositions(nCan) {\n let xCan = [], yCan = [];\n for (let n=0;n@mbostock`}`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":4,"value":"// Borrowed from https://observablehq.com/@mbostock/beta-distributed-random-values\n// retrieved 2019 March 8\nfunction randb(alpha, beta) {\n const u = randg(alpha);\n return u / (u + randg(beta));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":6,"value":"// Returns a gamma deviate by the method of Marsaglia and Tsang.\n// Borrowed from https://observablehq.com/@mbostock/beta-distributed-random-values\n// retrieved 2019 March 8\nfunction randg(shape) {\n let oalph = shape, a1, a2, u, v, x, mat;\n if (!shape) shape = 1;\n if (shape < 1) shape += 1;\n a1 = shape - 1 / 3;\n a2 = 1 / Math.sqrt(9 * a1);\n do {\n do {\n x = randn();\n v = 1 + a2 * x;\n } while (v <= 0);\n v = v * v * v;\n u = Math.random();\n } while (\n u > 1 - 0.331 * Math.pow(x, 4) &&\n Math.log(u) > 0.5 * x * x + a1 * (1 - v + Math.log(v))\n );\n if (shape === oalph) return a1 * v; // alpha > 1\n do u = Math.random(); while (u === 0); // alpha < 1\n return Math.pow(u, 1 / oalph) * a1 * v;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":8,"value":"// Returns a normal deviate (mu=0, sigma=1).\n// Borrowed from https://observablehq.com/@mbostock/beta-distributed-random-values\n// retrieved 2019 March 8\nfunction randn() {\n let u, v, x, y, q;\n do {\n u = Math.random();\n v = 1.7156 * (Math.random() - 0.5);\n x = u - 0.449871;\n y = Math.abs(v) + 0.386595;\n q = x * x + y * (0.19600 * y - 0.25472 * x);\n } while (q > 0.27597 && (q > 0.27846 || v * v > -4 * Math.log(u) * u * u));\n return v / u;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":212,"value":"md `--- ---\n*Colors to use*`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":196,"value":"colors = [\"red\", \"pink\", \"blue\", \"purple\", \"orange\", \"cyan\", \"magenta\", \"green\"];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":214,"value":"md `--- ---\n*Other helpful functions and constants*`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":242,"value":"function getMin(arr) {\n // Return the value and index of the smallest element in an array\n let minVal = Infinity;\n let minIdx;\n for (let n=0;n maxVal) {\n maxVal = arr[n]\n maxIdx = n;\n }\n }\n return [maxVal, maxIdx];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":14,"value":"import {slider,d3,addCircle,MakeStandardAxes,make_svg_path_from_data,text} from \"@ronzor/common\";","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"