Outcome error - Revision history

Woozle at 18:30, 8 August 2020

2020-08-08T18:30:19Z

Woozle at 01:08, 8 August 2020

2020-08-08T01:08:23Z

Woozle: not done

2020-08-07T21:16:30Z

not done

Woozle: Created page with "Outcome error is the difference between what voters want and what they actually get. It can apply to individuals (what one person wanted vs. what they got) as well as bein..."

2020-08-07T20:06:22Z

Created page with "Outcome error is the difference between what voters want and what they actually get. It can apply to individuals (what one person wanted vs. what they got) as well as bein..."

New page

[[Outcome error]] is the difference between what voters want and what they actually get. It can apply to individuals (what one person wanted vs. what they got) as well as being summed all participants in an election. The latter gives an idea of how well the voting system serves as a way of determining how well any given voting system serves the votership in any given circumstance.

Note that "want" is much more than just "I want Option X to win". Most voters have some idea of not only what outcome they'd most prefer, but also a range of other outcomes which would be acceptable, others which would be tolerable, and still others which would be bad or even absolutely unacceptable. In the event that Option X does win the election, the degree of ''individual'' [[outcome error]] goes up as we move from "preferred" to "absolutely unacceptable".

Range voting ''alone'' allows an unambiguous expression of this complexity for each of the possible options, allowing compromise so that (e.g.) an option that most people agree is ''tolerable'' could prevail, despite violent disagreement about which option would be ''best''.

@@ Line 71: / Line 71: @@
 | align=right | O<sub>o</sub>-O<sub>v</sub>: || align=right | +20 || align=right | -20 || align=right |   0 || (400+400+0)=800 || 28.3
 |}
-This does correctly reflect the fact that voter 1 is happier with the outcome than voter 2, that voter 3 is less happy than voter 2, that voter 4 is ''even'' less happy, and that voter 5 is ''slightly'' happier than voter 4 because they were ''really worried'' about an option which didn't win (whereas 4 didn't care much) but still less content than voter 3 (narrative unclear on this one; will have to think about it).
+This does correctly reflect the fact that voter 1 is happier with the outcome than voter 2, that voter 3 is less happy than voter 2, that voter 4 is ''even'' less happy, and that voter 5 is ''slightly'' happier than voter 4 because they were ''really worried'' about an option which didn't win (whereas 4 didn't care much) but still less content than voter 3 (who was neutral about option C, which lost, while 5 hated C and is a bit extra-glad it didn't win).
-NTS: should probably check these figures over again.
+A ''possible'' objection to this algorithm lies in the fact that {disapproval of an option which won} is weighted the same as {approval of an option which lost}. Further analysis needed.
 ==Footnote==
 <references>
 <ref name=winners>Some elections can have multiple winners; this particular example only allows one.</ref>
 </references>

@@ Line 18: / Line 18: @@
 Example, where we use a range from -10 to +10:
-{|
+{| border=1
 |-
 ! option &rarr; || A || B || C
 |-
-| '''voter 1''' ratings: || +10 || 0 || -10
+| '''voter 1''' ratings: || align=right | +10 || align=right |   0 || align=right | -10
 |-
-| '''voter 2''' ratings: || +5 || +10 || -5
+| '''voter 2''' ratings: || align=right |  +5 || align=right | +10 || align=right | -5
 |}
-If A wins:
+Let's play out the scenario where A wins:
 * '''Voter 1''' would seem to be completely satisfied. They're not going to object that B didn't win, because they were lukewarm about it, and they're delighted that C didn't win either. It seems fair to say that they're 100% satisfied with this outcome.
 * '''Voter 2''', however, is less sanguine. One of the options they liked (A) did win, and the one option they disliked (C) did not -- but there was another option they liked better (B) which didn't win. It seems fair to say that they have a positive feeling about the outcome, but less than 100%.
@@ Line 37: / Line 37: @@
 * Each losing option gets an outcome value ('''O<sub>o</sub>''') of '''-10'''.
 * Any winning option<ref name=winners /> gets a O<sub>o</sub> of '''+10'''.
-* We then take the difference between '''O<sub>o</sub>''' (the outcome for each option) and '''O<sub>v</sub>''' (how the voter felt about that option), and sum them across all options:
+* We then take the difference between '''O<sub>o</sub>''' (the outcome for each option) and '''O<sub>v</sub>''' (how the voter felt about that option), and sum them across all options - and since we want the ''magnitude'' of the disagreements to sum, we'll use RMS again:
-*# <code>SUM(O<sub>v</sub> - O<sub>o</sub>)</code> (summed across all votes for a given issue)
+*: <code>SQRT(SUM((O<sub>v</sub>)<sup>2</sup>-(O<sub>o</sub>)<sup>2</sup>)</code> (summed across all votes for a given issue) - dissatisfaction rating (0 = not at all dissatisfied; positive values = more dissatisfied)
 ==Footnote==
 <references>
 <ref name=winners>Some elections can have multiple winners; this particular example only allows one.</ref>
 </references>

← Older revision		Revision as of 21:16, 7 August 2020
Line 4:		Line 4:

	Range voting ''alone'' allows an unambiguous expression of this complexity for each of the possible options, allowing compromise so that (e.g.) an option that most people agree is ''tolerable'' could prevail, despite violent disagreement about which option would be ''best''.		Range voting ''alone'' allows an unambiguous expression of this complexity for each of the possible options, allowing compromise so that (e.g.) an option that most people agree is ''tolerable'' could prevail, despite violent disagreement about which option would be ''best''.
		+	==Terminology==
		+	* individual outcome error (for one voter): "individual outcome error", or '''E<sub>i</sub>'''
		+	* collective outcome error across all voters: "summed outcome error", or '''E<sub>all</sub>'''
		+	==Summing==
		+	There are at least a couple of different reasonable ways of calculating E<sub>all</sub>. My default is to use [[wikipedia:Root mean square\|RMS]]:
		+	:<code>SUM((E<sub>i</sub>^2)^0.5)</code> (summed across all votes for a given issue)
		+
		+	In any system where voters can express a position on more than one candidate (this applies both to range voting ''and'' ranked voting), we also need to sum up those positions to determine how much they disagree with the winning choice. This calculation depends on the ''meaning'' of those expressions, or (more precisely) what meaning the voter is trying to express ''through'' them.
		+	===Range Voting===
		+	In the case of range voting with a range from -X to +X, the meaning is pretty obvious: minus X indicates the strongest disapproval, and plus X represents the strongest approval.
		+
		+	Another question which arises is whether we count the voter's opinions on choices which ''didn't'' win.
		+
		+	Example, where we use a range from -10 to +10:
		+	{\|
		+	\|-
		+	! option → \|\| A \|\| B \|\| C
		+	\|-
		+	\| '''voter 1''' ratings: \|\| +10 \|\| 0 \|\| -10
		+	\|-
		+	\| '''voter 2''' ratings: \|\| +5 \|\| +10 \|\| -5
		+	\|}
		+	If A wins:
		+	* '''Voter 1''' would seem to be completely satisfied. They're not going to object that B didn't win, because they were lukewarm about it, and they're delighted that C didn't win either. It seems fair to say that they're 100% satisfied with this outcome.
		+	* '''Voter 2''', however, is less sanguine. One of the options they liked (A) did win, and the one option they disliked (C) did not -- but there was another option they liked better (B) which didn't win. It seems fair to say that they have a positive feeling about the outcome, but less than 100%.
		+
		+	For the sake of working out an algorithm to calculate this:
		+	* Let's call the voter's ranking for each option the "option's voter-rating", '''O<sub>v</sub>'''.
		+	* Let's call the value assigned to each option to express how it did in the election the "option's outcome-value" ('''O<sub>o</sub>''')
		+
		+	An algorithm which seems to result in this unitary evaluation of each voter's satisfaction would be:
		+	* Each losing option gets an outcome value ('''O<sub>o</sub>''') of '''-10'''.
		+	* Any winning option<ref name=winners /> gets a O<sub>o</sub> of '''+10'''.
		+	* We then take the difference between '''O<sub>o</sub>''' (the outcome for each option) and '''O<sub>v</sub>''' (how the voter felt about that option), and sum them across all options:
		+	*# <code>SUM(O<sub>v</sub> - O<sub>o</sub>)</code> (summed across all votes for a given issue)
		+	==Footnote==
		+	<references>
		+	<ref name=winners>Some elections can have multiple winners; this particular example only allows one.</ref>
		+	</references>