{"id":8865,"date":"2023-10-11T18:21:19","date_gmt":"2023-10-11T18:21:19","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=8865"},"modified":"2024-10-18T20:58:34","modified_gmt":"2024-10-18T20:58:34","slug":"voting-theory-learn-it-5","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/voting-theory-learn-it-5\/","title":{"raw":"Voting Theory: Learn It 5","rendered":"Voting Theory: Learn It 5"},"content":{"raw":"

Approval Voting<\/h2>\r\n

Up until now, we\u2019ve been considering voting methods that require ranking of candidates on a preference ballot. There is another method of voting that can be more appropriate in some decision making scenarios.<\/p>\r\n

\r\n
\r\n

approval voting<\/h3>\r\n

With approval voting<\/strong>, the ballot asks you to mark all choices that you find acceptable. The results are tallied, and the option with the most approval is the winner.<\/p>\r\n<\/div>\r\n<\/section>\r\n

Let's take a look at an example.<\/p>\r\n

A group of mathematicians are getting together for a conference. The members are coming from four cities: Seattle, Tacoma, Puyallup, and Olympia. Their votes are tallied below. Find the winner using Approval voting.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\u00a0<\/td>\r\n[latex]30[\/latex]<\/td>\r\n[latex]10[\/latex]<\/td>\r\n[latex]15[\/latex]<\/td>\r\n[latex]20[\/latex]<\/td>\r\n[latex]15[\/latex]<\/td>\r\n[latex]5[\/latex]<\/td>\r\n[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n
Seattle<\/td>\r\nX<\/td>\r\nX<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\n\u00a0<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\n<\/tr>\r\n
Tacoma<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\nX<\/td>\r\nX<\/td>\r\nX<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\n<\/tr>\r\n
Puyallup<\/td>\r\n\u00a0<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\nX<\/td>\r\nX<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\n<\/tr>\r\n
Olympia<\/td>\r\n\u00a0<\/td>\r\n\u00a0<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\nX<\/td>\r\n\u00a0<\/td>\r\nX<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n[reveal-answer q=\"109152\"]Solution[\/reveal-answer] [hidden-answer a=\"109152\"]\r\n\r\n

Seattle has [latex]30+10+15+5 = 60[\/latex] approval votes.<\/p>\r\n

Tacoma has [latex]30+15+20+15+5 = 85[\/latex] approval votes.<\/p>\r\n

Puyallup has [latex]10+20+15+5 = 50[\/latex] approval votes.<\/p>\r\n

Olympia has [latex]15+15+5 = 35[\/latex] approval votes.<\/p>\r\n

Tacoma wins under this approval voting.<\/p>\r\n\r\n[\/hidden-answer]<\/section>\r\n

[ohm2_question hide_question_numbers=1]13080[\/ohm2_question]<\/section>\r\n

What\u2019s Wrong with Approval Voting?<\/h3>\r\n

Approval voting can very easily violate the majority criterion. Let's explore this through an example.<\/p>\r\n

Consider the voting schedule:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
 <\/td>\r\n[latex]80[\/latex]<\/td>\r\n[latex]15[\/latex]<\/td>\r\n[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n
1st choice<\/td>\r\nA<\/td>\r\nB<\/td>\r\nC<\/td>\r\n<\/tr>\r\n
2nd choice<\/td>\r\nB<\/td>\r\nC<\/td>\r\nB<\/td>\r\n<\/tr>\r\n
3rd choice<\/td>\r\nC<\/td>\r\nA<\/td>\r\nA<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

 <\/p>\r\n

Clearly A is the majority winner. Now suppose that this election was held using approval voting, and every voter marked approval of their top two candidates. A would receive approval from [latex]80[\/latex] voters B would receive approval from [latex]100[\/latex] voters C would receive approval from [latex]20[\/latex] voters B would be the winner. Some argue that Approval Voting tends to vote the least disliked choice, rather than the most liked candidate.<\/p>\r\n<\/section>\r\n

Additionally, approval voting is susceptible to strategic insincere voting, in which a voter does not vote their true preference to try to increase the chances of their choice winning.<\/p>","rendered":"

Approval Voting<\/h2>\n

Up until now, we\u2019ve been considering voting methods that require ranking of candidates on a preference ballot. There is another method of voting that can be more appropriate in some decision making scenarios.<\/p>\n

\n
\n

approval voting<\/h3>\n

With approval voting<\/strong>, the ballot asks you to mark all choices that you find acceptable. The results are tallied, and the option with the most approval is the winner.<\/p>\n<\/div>\n<\/section>\n

Let’s take a look at an example.<\/p>\n

A group of mathematicians are getting together for a conference. The members are coming from four cities: Seattle, Tacoma, Puyallup, and Olympia. Their votes are tallied below. Find the winner using Approval voting.<\/p>\n\n\n\n\n\n\n\n
\u00a0<\/td>\n[latex]30[\/latex]<\/td>\n[latex]10[\/latex]<\/td>\n[latex]15[\/latex]<\/td>\n[latex]20[\/latex]<\/td>\n[latex]15[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n[latex]5[\/latex]<\/td>\n<\/tr>\n
Seattle<\/td>\nX<\/td>\nX<\/td>\nX<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\nX<\/td>\n\u00a0<\/td>\n<\/tr>\n
Tacoma<\/td>\nX<\/td>\n\u00a0<\/td>\nX<\/td>\nX<\/td>\nX<\/td>\nX<\/td>\n\u00a0<\/td>\n<\/tr>\n
Puyallup<\/td>\n\u00a0<\/td>\nX<\/td>\n\u00a0<\/td>\nX<\/td>\nX<\/td>\nX<\/td>\n\u00a0<\/td>\n<\/tr>\n
Olympia<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\nX<\/td>\n\u00a0<\/td>\nX<\/td>\n\u00a0<\/td>\nX<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n