24:null 25:["$","title",null,{"children":"District vs. Proportional Representation | RJ Sheperd | Observable"}] 2a:T714,md`# District vs. Proportional Representation Portlanders are considering moving from an At-Large style to a District-based representation system. While district-based representation has the benefit of serving the interests of a particular geographic boundary, this system can be used to disenfranchise voters through [gerrymandering](https://en.wikipedia.org/wiki/Gerrymandering), thus enabling a minority of the population to obtain a majority of the votes (as seen in North Carolina) and to over-represent land instead of population (as seen in the U.S. Senate). Support for district based representation has been proposed to ensure representation for BIPOC communities, but as [Portland City Club's New Government Report](https://drive.google.com/open?id=1y74WRaWJA3j2QEYqsAOtZwcLOvT97VcZ) notes, our BIPOC communities are too spread out geographically to guarantee a BIPOC commissioner even with a heavily gerrymandered district. An alternative that is often not talked about is [Proportional Representation](https://en.wikipedia.org/wiki/Proportional_representation). In proportional representation, votes are cast for a particular party, with the number of seats assigned to each party based on the percentage of total votes cast. In Proportional Representation, minority^* parties have a much higher chance of obtaining at least one seat. This simulation uses data from the 2020 Portland primary election. Commissioners can be from one of five political parties: Purple, Orange, Green, Teal, and Pink. The Pink Party will be our minority^* party. The percentage of voters from each party is generated at the begging of the simulation. ^*By minority, I refer to the technical definition of a smaller number of voters, not an ethnic or racial minority. `2b:T402,proportional_seats = { let seats = { orange: 0, teal: 0, green: 0, purple: 0, pink: 0 }; function addSeat(party) { seats[party] += 1; } // de-Hondt Method (V / 2s + 1) // Webster Method (V / 2s + 1) function quotient(party, votes) { const denominator = 2 * seats[party] + 1; return votes / denominator; } function seatsAllocated() { return Object.values(seats).reduce((a, b) => a + b, 0); } function largestQuotientParty(quotients) { let max = 0; let max_party = ''; quotients.map(q => { if (q.quotient > max) { max = q.quotient; max_party = q.party; } }); return max_party; } function allocateSeats() { while (total_seats - seatsAllocated() > 0) { let quotients = Object.keys(proportional).map(k => ({ party: k, quotient: quotient(k, proportional[k]) })); let party = largestQuotientParty(quotients); addSeat(party); } } allocateSeats(); return seats; }2c:[] 28:{"id":"ee1af1e388e5b921","slug":"district-vs-proportional-representation","title":"District vs. Proportional Representation","thumbnail":"75450e0833df9529b473013db944beb0081b5656d5e075a286f2fbacf9528e60","access_level":"public","create_time":"$D2020-08-14T18:28:24.472Z","update_time":"$D2020-08-15T00:10:51.655Z","view_time":null,"first_public_time":"$D2020-08-14T23:48:41.885Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"17bf59a69dd03155","login":"rjsheperd","name":"RJ Sheperd","avatar_url":"https://avatars-next.observableusercontent.com/e04d70557fc7a197e679f88c7139bd1e35ae16bf9f56b711298fa41ba5669fe2","tier":"starter_2024"},"version":450,"publish_version":450,"role":null,"authored":false,"authors":[{"type":"individual","id":"9449957e349b2b2f","login":"rjsheperd","name":"RJ Sheperd","avatar_url":"https://avatars-next.observableusercontent.com/e04d70557fc7a197e679f88c7139bd1e35ae16bf9f56b711298fa41ba5669fe2","tier":null}],"members":[{"type":"individual","id":"9449957e349b2b2f","login":"rjsheperd","name":"RJ Sheperd","avatar_url":"https://avatars-next.observableusercontent.com/e04d70557fc7a197e679f88c7139bd1e35ae16bf9f56b711298fa41ba5669fe2","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"1bfe063d2add409d","slug":"elections","title":"Elections","owner":{"id":"17bf59a69dd03155","login":"rjsheperd","name":"RJ Sheperd"}},"type":"notebook","body":{"title":"District vs. Proportional Representation","cells":[{"id":0,"value":"$2a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":9,"value":"viewof total_seats = slider({\n title: \"Commissioners\",\n min: 5,\n max: 25,\n step: 1\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":121,"value":"md`Each Commissioner represents: **${num(\n Math.round(pop_represents)\n)} Portlanders, or ${num(Math.round(voters_represents))} registered voters **`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":362,"value":"md`We start by splitting the total population into parties:\n- Purple: ${Math.round(parties.purple)}% (${num(\n Math.round(registered_voters * (parties.purple / 100))\n)} voters)\n- Orange: ${Math.round(parties.orange)}% (${num(\n Math.round(registered_voters * (parties.orange / 100))\n)} voters)\n- Teal: ${Math.round(parties.teal)}% (${num(\n Math.round(registered_voters * (parties.teal / 100))\n)} voters)\n- Green: ${Math.round(parties.green)}% (${num(\n Math.round(registered_voters * (parties.green / 100))\n)} voters)\n- Pink: ${Math.round(pink)}% (${num(\n Math.round(registered_voters * (pink / 100))\n)} voters)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":379,"value":"md`### District-Based Representation\n\nTo simulate districts, we randomly allocate these voters into ${total_seats} districts:\n\n|District|Purple Party|Orange Party|Teal Party|Green party|Pink Party|\n|--------|--|--|--|--|--|\n${districts_randomized_voters\n .map(\n (d, i) =>\n `|District ${num(i + 1)}|${num(d.purple)}|${num(d.orange)}|${num(\n d.teal\n )}|${num(d.green)}|${num(d.pink)}|`\n )\n .join('\\n')}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":352,"value":"md`In a District-Based system, each district's seat goes to the party with the most votes:\n\n| |Purple Party|Orange Party|Teal Party|Green party|Pink Party|\n|--------|--|--|--|--|--|\n|Commissioners|${district_seats.purple}|${district_seats.orange}|${\n district_seats.teal\n}|${district_seats.green}|${district_seats.pink}|\n\nUnfortunately, this means the Pink party is left with zero representation, even though they make up ${Math.round(\n pink\n)}% of the population.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":355,"value":"md`### Proportional System\n\nIn a Proportional system, the number of seats are assigned proportionally:\n\n| |Purple Party|Orange Party|Teal Party|Green party|Pink Party|\n|--------|--|--|--|--|--|\n|Commissioners|${proportional_seats.purple}|${proportional_seats.orange}|${proportional_seats.teal}|${proportional_seats.green}|${proportional_seats.pink}|`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":359,"value":"md`In a Proportional Representation system, the Pink minority party would gain ${proportional_seats.pink -\n district_seats.pink} seats. \n\nThe Proportional Representation system also more equally distributed the seats among the \"major\" parties, rather than leaving it up to how district boundaries are drawn.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":427,"value":"md`## Further Reading\n\nThis is not the first time Proportional Representation has been considered in America. Here are some other pieces I recommend:\n* Santucci, Jack. “Why Adopting Proportional Voting May Bring Back the Big-Tent Political Party.” USAPP, November 5, 2018. https://blogs.lse.ac.uk/usappblog/2018/11/05/why-adopting-proportional-voting-may-bring-back-the-big-tent-political-party/.\n* Board, The Editorial. “A Congress for Every American.” The New York Times, November 10, 2018, sec. Opinion. https://www.nytimes.com/interactive/2018/11/10/opinion/house-representatives-size-multi-member.html\n\nAnother impact of District-Based Representation is that housing production decreases:\n* Mast, Evan. “[Why Do NIMBYs Win? Local Control and Housing Supply](https://www.dropbox.com/s/76jq4x0x2yc2c54/mast_at_large_ward.pdf)”. December, 2019. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":411,"value":"md`

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":199,"value":"md`## Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":3,"value":"population = 654741 // 2019 Census","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":34,"value":"registered_voters = 440482","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":35,"value":"ballots_received = 174808","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":134,"value":"voters_represents = registered_voters / total_seats","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":12,"value":"pop_represents = population / total_seats","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":202,"value":"md`### Parties`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":102,"value":"colors = ({\n green: '#a1d76a',\n pink: '#e9a3c9',\n orange: '#f1a340',\n purple: '#998ec3'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":69,"value":"parties = ({\n purple: party_gen(),\n green: party_gen(),\n orange: party_gen(),\n teal: party_gen()\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":96,"value":"pink = 100 - Object.values(parties).reduce((a, b) => a + b, 0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":205,"value":"md`### Proportional`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":107,"value":"proportional = {\n let votes = {};\n Object.keys(parties).forEach(\n k => (votes[k] = Math.round(ballots_received * (parties[k] / 100)))\n );\n votes['pink'] = Math.round(ballots_received * (pink / 100));\n return votes;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":158,"value":"$2b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":227,"value":"md`### Districts`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":235,"value":"districts_equal_voters = Array(15).fill({\n purple: Math.round(proportional.purple / 15),\n green: Math.round(proportional.green / 15),\n orange: Math.round(proportional.green / 15),\n teal: Math.round(proportional.teal / 15),\n pink: Math.round(proportional.pink / 15)\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":247,"value":"districts_randomized_voters = {\n const districts = [];\n const seed = {\n purple: seedVoters('purple'),\n green: seedVoters('green'),\n orange: seedVoters('orange'),\n teal: seedVoters('teal'),\n pink: seedVoters('pink')\n };\n\n for (let i = 0; i < total_seats; i++) {\n districts.push({\n purple: seed['purple'][i],\n green: seed['green'][i],\n orange: seed['orange'][i],\n teal: seed['teal'][i],\n pink: seed['pink'][i]\n });\n }\n\n return districts;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":322,"value":"district_seats = districts_randomized_voters\n .map(district => {\n return Object.keys(district).reduce(\n (max, k) => (max[1] > district[k] ? max : [k, district[k]]), // emit [party, count]\n [null, 0]\n )[0]; // Get only the party name\n })\n .reduce(\n (obj, k) => {\n obj[k]++;\n return obj;\n },\n {\n purple: 0,\n green: 0,\n orange: 0,\n teal: 0,\n pink: 0\n }\n )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":344,"value":"district_seats","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":222,"value":"md`### Utils`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":85,"value":"party_gen = d3.randomUniform(20, 25)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":254,"value":"district_pop_gen = d3.randomUniform(0, 1 / (total_seats / 2))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":282,"value":"district_pop_gen()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":266,"value":"function seedVoters(party) {\n const total_votes = proportional[party];\n const districts = [];\n const avg_votes = Math.round(total_votes / total_seats);\n\n for (let i = 0; i < total_seats; i++) {\n let district = Math.round(district_pop_gen() * total_votes);\n while (district > avg_votes) {\n district = Math.round(district_pop_gen() * total_votes);\n }\n districts.push(district);\n }\n\n const votes_left = total_votes - districts.reduce((a, b) => a + b, 0);\n if (votes_left > 0) {\n const added_votes = Math.round(votes_left / total_seats);\n return districts.map(d => d + added_votes);\n }\n\n return districts;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":438,"value":"num = {\n const formatter = new Intl.NumberFormat('en-EN', {\n useGrouping: true,\n maximumFractionDigits: 0\n });\n return formatter.format;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":79,"value":"md`### Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":7,"value":"import { slider } from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":82,"value":"d3 = require('d3')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W2c","stdlib":"1","titling":"auto"}} 29:"$28:body"