基數投票制

基數投票制指任何允許選民分別評估每位候選人的選舉制度，通常爲分數或等級的評價。這些選舉制度也被稱爲「評分」（評分投票）、「評估」、「評級」或「絕對」投票制。基於基數效用的基數制與基於序數效用（英语：Ordinal utility）的序數制，是除多數制外，現代投票制度的兩大類別。 多種投票制度允許選民分別評估每位候選人，如： 贊成投票（英語：approval rating，AV），最簡單的制度，祇允許 2 個等級（0、1）：「贊成」與「不贊成」。 評估投票（英語：evaluated rating，EV）或混合贊成投票（英语：combined approval voting）（英語：combined approval rating，CAV），採用 3 個等級（−1、0、+1）：「反對」、「棄權」與「支持」。 計分投票或範圍投票，以數字評分，擁有最高的平均或總和評分的候選人獲勝。 計分投票採用離散的整數尺度，通常爲 0–5 或 0–9。 範圍投票採用 0–1 連續的尺度。 最高中位數規則（英语：Highest median voting rules），選舉具有最高中位數評級的候選人。不同的最高中位數規則，以不同的方法打破平局。多數判斷（英语：majority judgment）的等級以詞語表述，如「優秀」至「差」。多數判斷是最高中位數規則最常見的例子，因爲它在此類規則中最早被研究，但此後也有其他規則被提出，如典型判斷與常規判斷（英语：Usual judgment）。 STAR投票（英语：STAR voting），評分爲 0–5。總分最高的兩名候選人，在多數投票中評分更高的一位獲勝。 多數贊成投票，巴克林投票計分的變體，通常使用字母等級，如「A」至「F」。 3-2-1 投票，投票者評價每位候選人爲「好」、「尚可」或「壞」。投票結果以三個自動淘汰步驟計算：第一步選擇「好」評分最多的三位候選人。第二步選擇「壞」最少的兩位。最後一步，大多數人喜歡的一位獲勝。 此外，數個基數制具有多勝者選舉的變體，通常是爲了達到比例代表，如： 比例贊成投票（英语：Proportional approval voting） 順序比例贊成投票（英语：Sequential proportional approval voting） 滿意贊成投票（英语：Satisfaction approval voting） 重新加權範圍投票 基數 波達計數法 Baujard, Antoinette; Gavrel, Frédéric; Igersheim, Herrade; Laslier, Jean-François; Lebon, Isabelle. How voters use grade scales in evaluative voting (PDF). European Journal of Political Economy. 2017-09, 55: 14–28 [2021-09-04]. ISSN 0176-2680. doi:10.1016/j.ejpoleco.2017.09.006. （原始内容 (PDF)存档于2022-05-12） （英语）. A key feature of evaluative voting is a form of independence: the voter can evaluate all the candidates in turn . . . another feature of evaluative voting . . . is that voters can express some degree of preference.  Cardinal voting systems. Electowiki. [2017-01-31]. （原始内容存档于2022-02-22） （英语）.  Voting system. Electowiki. [2017-01-31]. （原始内容存档于2021-12-19） （英语）.  Riker, William Harrison. Liberalism against populism: A confrontation between the theory of democracy and the theory of social choice. Waveland Pr. 1982: 29–30. ISBN 0881333670. OCLC 316034736 （英语）. Ordinal utility is a measure of preferences in terms of rank orders—that is, first, second, etc. . . . Cardinal utility is a measure of preferences on a scale of cardinal numbers, such as the scale from zero to one or the scale from one to ten.  Ordinal versus cardinal voting rules: A mechanism design approach （英语）.  Vasiljev, Sergei. Cardinal voting: The way to escape the social choice impossibility. 2008-04. SSRN 1116545  （英语）.  Hillinger, Claude. The case for utilitarian voting. Open Access LMU. 2005-05-01 [2018-05-15]. （原始内容存档于2020-04-25） （英语）. Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores −1, 0, 1.  Hillinger, Claude. On the possibility of democracy and rational collective choice. Rochester, NY. 2004-10-01. SSRN 608821  （英语）. I favor 'evaluative voting' under which a voter can vote for or against any alternative, or abstain.  Felsenthal, Dan S. On combining approval with disapproval voting. Behavioral Science. 1989-01, 34 (1): 53–60. ISSN 0005-7940. doi:10.1002/bs.3830340105 （英语）. under CAV he has three options—cast one vote in favor, abstain, or cast one vote against.  Range Voting. Social Choice and Beyond. [2016-12-10]. （原始内容存档于2016-08-25） （英语）. with the winner being the one with the largest point total. Or, alternatively, the average may be computed and the one with the highest average wins  Score Voting. The Center for Election Science. 2015-05-21 [2016-12-10]. （原始内容存档于2019-01-25） （英语）. Simplified forms of score voting automatically give skipped candidates the lowest possible score for the ballot they were skipped. Other forms have those ballots not affect the candidate’s rating at all. Those forms not affecting the candidates rating frequently make use of quotas. Quotas demand a minimum proportion of voters rate that candidate in some way before that candidate is eligible to win.  Should you be using a more expressive voting system?. VoteUp. [2018-05-15]. （原始内容存档于2017-09-09） （英语）. Score Voting—it's just like range voting except the scores are discrete instead of spanning a continuous range.  Rating scale research. RangeVoting.org. [2018-05-15]. （原始内容存档于2019-05-07） （英语）. The present page seems to conclude 0-9 is the best scale.  Good criteria support range voting. RangeVoting.org. [2018-05-15]. （原始内容存档于2018-05-16） （英语）. Definition 1: For us "Range voting" shall mean the following voting method. Each voter provides as her vote, a set of real number scores, each in [0,1], one for each candidate. The candidate with greatest score-sum, is elected.  Smith, Warren D. Range voting (PDF). 2000-12 [2021-09-04]. （原始内容 (PDF)存档于2018-08-20） （英语）. The “range voting” system is as follows. In a c-candidate election, you select a vector of c real numbers, each of absolute value ≤1, as your vote. E.g. you could vote (+1, −1, +.3, −.9, +1) in a five-candidate election. The vote-vectors are summed to get a c-vector x and the winner is the i such that xi is maximum.  Balinski, Michel; Laraki, Rida. A theory of measuring, electing, and ranking. 美國國家科學院院刊. 2007, 104 (21): 8720–8725. PMC 1885569 . PMID 17496140. doi:10.1073/pnas.0702634104 （英语）.  Fabre, Adrien. Tie-breaking the highest median: Alternatives to the majority judgment (PDF). Social Choice and Welfare. 2020. doi:10.1007/s00355-020-01269-9 （英语）.  STAR Voting. Equal Vote Coalition. [2018-07-14]. （原始内容存档于2020-07-01） （英语）.  STAR voting an intriguing innovation. The Register Guard. [2018-07-14]. （原始内容存档于2018-08-06） （英语）.  Are we witnessing the cutting edge of voting reform?. Independent voter news. 2018-02-01 [2018-07-14]. （原始内容存档于2021-02-10） （美国英语）.  Majority approval voting. Electowiki. [2018-08-26]. （原始内容存档于2021-04-20） （英语）.  3-2-1 voting. Electowiki. [2021-09-04]. （原始内容存档于2022-04-16） （英语）.  Quinn, Jameson. Make. All. Votes. Count. (Part II: Single-winner). Jameson Quinn. 2017-05-28 [2018-07-14]. （原始内容存档于2021-04-10） （英语）.  Reweighted range voting – A PR voting method that feels like range voting. RangeVoting.org. [2018-03-24]. （原始内容存档于2019-06-18） （英语）.