Task:Define voting procedure for Community Council elections - Revision history

imported_>allnameswereout at 13:06, 29 October 2009

2009-10-29T13:06:38Z

← Older revision		Revision as of 13:06, 29 October 2009
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	[[Category:Community]]		[[Category:Community]]
	[[Category:maemo.org]]		[[Category:maemo.org]]
	[[Category:Council]]		[[Category:Community Council]]

imported_>dneary: /* Proposal: Single Transferable Vote */

2008-12-03T19:41:14Z

Proposal: Single Transferable Vote

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	* Q (the quota) = floor(T/(N+1) + 1)		* Q (the quota) = floor(T/(N+1) + 1)

	[http://en.wikipedia.org/wiki/Single_transferable_vote Single transferable vote] is the voting system used in Ireland's general elections, with multi-seat constituencies resembling a Maemo Community Council vote - there are N places and C candidates, with C > N.		[http://en.wikipedia.org/wiki/Single_transferable_vote Single transferable vote] is the voting system used in Ireland's general elections, with multi-seat constituencies resembling a Maemo Community Council vote - there are N places and C candidates, with C > N. There is an added advantage of having [http://stv.sourceforge.net/ software available to count STV].

	The voting system is simple from the voter's point of view - you vote in order of preference for one or more of the candidates. If you only have a first preference, you vote only 1 for your choice. If you have a second preference, you give him number 2, and you continue like this down the ballot, as far as you care to go.		The voting system is simple from the voter's point of view - you vote in order of preference for one or more of the candidates. If you only have a first preference, you vote only 1 for your choice. If you have a second preference, you give him number 2, and you continue like this down the ballot, as far as you care to go.

imported_>dneary: /* Proposal: Single Transferable Vote */

2008-12-03T19:09:39Z

Proposal: Single Transferable Vote

← Older revision		Revision as of 19:09, 3 December 2008
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	# C, A		# C, A
	# C		# C
	* D, C		# D, C

	1st count:		1st count:

imported_>dneary: Describe STV.

2008-12-03T19:09:03Z

Describe STV.

← Older revision		Revision as of 19:09, 3 December 2008
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	''b''<sub>''ij''(''k''+1)</sub>=''a<sub>ij</sub>'' / ( 1 + ∑<sub>''p''∈(1…''k'')</sub> ''a<sub>iw<sub>p</sub></sub>'' )		''b''<sub>''ij''(''k''+1)</sub>=''a<sub>ij</sub>'' / ( 1 + ∑<sub>''p''∈(1…''k'')</sub> ''a<sub>iw<sub>p</sub></sub>'' )

			== Proposal: Single Transferable Vote ==

			Notation:
			* N seats available
			* C candidates running
			* T total valid votes cast in the election
			* Q (the quota) = floor(T/(N+1) + 1)

			[http://en.wikipedia.org/wiki/Single_transferable_vote Single transferable vote] is the voting system used in Ireland's general elections, with multi-seat constituencies resembling a Maemo Community Council vote - there are N places and C candidates, with C > N.

			The voting system is simple from the voter's point of view - you vote in order of preference for one or more of the candidates. If you only have a first preference, you vote only 1 for your choice. If you have a second preference, you give him number 2, and you continue like this down the ballot, as far as you care to go.

			Counting is also quite simple. We first count all the number 1 votes, and rank the candidates in order. If any candidates have more than T/(N+1) votes, they are deemed elected. Their surplus votes (the votes over the quota Q) are redistributed according to the weighings of their second preferences.

			If no-one has been deemed elected, or all surpluses have been distributed, the candidate with the least first preferences is eliminated, and his votes are redistributed according to the second preference.

			This process is repeated until N candidates are deemed elected, or until there are only 2 unelected candidates remaining. In this situation, the candidate with the highest number of votes is deemed elected without having reached the quota.

			A simple example will illustrate:

			4 candidates (A, B, C), 2 seats, 11 votes, the quota is thus 4 votes.

			# A, B
			# A, C
			# A
			# A, B, C
			# B, C
			# B, A
			# B, C
			# C
			# C, A
			# C
			* D, C

			1st count:
			* A: 4
			* B: 3
			* C: 3
			* D: 1

			A is deemed elected, and D is eliminated.

			D's 2nd preferences give 1 vote to C.

			2nd count:
			* A: 4
			* B: 3
			* C: 4

			A and C are deemed elected.

	== Discussions ==		== Discussions ==

imported_>generalantilles at 14:55, 3 December 2008

2008-12-03T14:55:35Z

← Older revision		Revision as of 14:55, 3 December 2008
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	{{task\|~~ongoing~~}}		{{task\|completed}}

imported_>benson: Add reference link

2008-12-03T08:21:48Z

Add reference link

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	== Proposal: RRV ==		== Proposal: RRV ==
			[http://scorevoting.net/RRV.html Background from scorevoting.net]

	I've added a description of [http://en.wikipedia.org/wiki/Range_voting#Reweighted_range_voting RRV] to Wikipedia. Since TeX isn't enabled here, it's easiest to read it there. (Provided, of course, it remains intact...)		I've added a description of [http://en.wikipedia.org/wiki/Range_voting#Reweighted_range_voting RRV] to Wikipedia. Since TeX isn't enabled here, it's easiest to read it there. (Provided, of course, it remains intact...)

	The proposal is edited for html legibility and simplicity below...		The proposal is edited for html legibility and simplicity below, but should be a complete specification.

	=== Variables ===		=== Variables ===

imported_>benson: /* Proposal: RRV */ HTMLized

2008-12-03T08:17:29Z

Proposal: RRV: HTMLized

← Older revision		Revision as of 08:17, 3 December 2008
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	== Proposal: RRV ==		== Proposal: RRV ==
			I've added a description of [http://en.wikipedia.org/wiki/Range_voting#Reweighted_range_voting RRV] to Wikipedia. Since TeX isn't enabled here, it's easiest to read it there. (Provided, of course, it remains intact...)

			The proposal is edited for html legibility and simplicity below...

	=== Variables ===		=== Variables ===
	*~~<math>~~l~~</math>~~: number of voters		*''l'': number of voters
	*~~<math>~~m~~</math>~~: number of candidates		*''m'': number of candidates
	*~~<math>~~n~~</math>~~: number of seats		*''n'': number of seats
	*~~<math>~~i~~</math>~~: index of voters (~~<math>~~1 \le i \le l~~</math>~~)		*''i'': index of voters (1 ≤ ''i'' ≤ ''l'')
	*~~<math>~~j~~</math>~~: index of candidates (~~<math>~~1 \le j \le m~~</math>~~)		*''j'': index of candidates (1 ≤ ''j'' ≤ ''m'')
	*~~<math>~~k~~</math>~~: index of seats (and rounds) (~~<math>~~1 \le k \le n~~</math>~~)		*''k'': index of seats (and rounds) (1 ≤ ''k'' ≤ ''n'')
	=== Parameters ===		=== Parameters ===
	~~A range for votes is selected by two limits, <math>a_{max}</math> and <math>a_{min}</math>.~~		An unbalanced normalized range is to be used, ranging from 0 to 1.
	~~Reasonable choices include:~~
	*<math>a_{min}=0</math>, <math>a_{max}=1</math> (unbalanced, normalized)
	*<math>a_{min}=-1</math>, <math>a_{max}=1</math> (balanced)
	*<math>a_{min}=0</math>, <math>a_{max}=100</math> (unbalanced percentage; potentially useful if ratings were to be quantized)
	~~The effects of the voting system are generally independent of the limits selected, but a balanced~~ range ~~''may'' be preferred by some voters to permit unknown candidates~~ to be ~~rated 0 with known~~, disliked candidates rated negative. Obviously this effect may be accomplished in an unbalanced range by rating unknown candidates <math>\tfrac{a_{min} + a_{max}}{2}</math>. Some calculations are simplified by using the unbalanced, normalized range, which makes it preferable from ~~a numerical perspective~~.

	A ballot from voter ~~<math>~~i~~</math>~~ consists of ~~<math>~~m~~</math>~~ ratings <~~math~~>~~a_{~~ij}</~~math~~> for the ~~<math>~~m~~</math>~~ candidates, such that <~~math~~>~~a_{min} \le a_{~~ij~~} \le a_{max}~~</~~math~~>.		A ballot from voter ''i'' consists of ''m'' ratings ''a<sub>ij</sub>'' for the ''m'' candidates, such that 0 ≤ ''a<sub>ij</sub>'' ≤ 1.

	=== Procedure ===		=== Procedure ===
	After all ballots are collected, ~~<math>~~n~~</math>~~ rounds are held to choose the winners <~~math~~>~~w_{~~k}</~~math~~>, with one winner chosen per round. In the first round, the weighted ratings for each voter are initialized as <~~math~~>~~b_{~~ij1}=~~a_{~~ij}</~~math~~>. The weighted scores in each round are summed:		After all ballots are collected, ''n'' rounds are held to choose the winners ''w<sub>k</sub>'', with one winner chosen per round. In the first round, the weighted ratings for each voter are initialized as ''b<sub>ij1</sub> = a<sub>ij</sub>''. The weighted scores in each round are summed:

	<~~math~~>~~B_{~~jk}=~~\sum_{~~i=1~~}^{~~l~~}b_{~~ijk}</~~math~~>		''B<sub>jk</sub>'' = ∑<sub>''i''∈(1…''l'')</sub>'' b<sub>ijk</sub>''

	The highest-scoring candidate not yet elected wins; this is not simple to express formally:		The highest-scoring candidate not yet elected wins; this is not simple to express formally:

	<~~math~~>~~w_k~~ = \max ( ~~B_{~~jk~~} \ni~~ j \notin ~~w_{~~1 ~~\cdots~~ k-1})</~~math~~>		''w<sub>k</sub>'' = max ( ''B<sub>jk</sub>'' s.t. ''j'' ∉ ''w''<sub>1…(''k''-1)</sub>)

	The weighted scores for each succeeding round are calculated by de-emphasizing ballots according to the portion in which they've already won:		The weighted scores for each succeeding round are calculated by de-emphasizing ballots according to the portion in which they've already won:

	<~~math~~>~~b_{~~ij(k+1)~~}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}-a_{min}}{a_{max}-a_{min}}}~~</~~math~~>		''b''<sub>''ij''(''k''+1)</sub>=''a<sub>ij</sub>'' / ( 1 + ∑<sub>''p''∈(1…''k'')</sub> ''a<sub>iw<sub>p</sub></sub>'' )

	~~In the case of an unbalanced range (~~<~~math~~>~~a_{min} = 0~~</~~math~~>~~), <math>b_{ij~~(~~k+1)}=\frac{a_{ij}}{~~1+~~\sum_{~~p=1~~}^{~~k~~}\tfrac{a_{iw_p}}{a_{max}}}~~</~~math~~>~~, and in the normalized case (~~<~~math~~>~~a_{max} = 1~~<~~/math~~>), <~~math~~>~~b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}a_{iw_p}}~~</~~math~~>.

	== Discussions ==		== Discussions ==

imported_>benson: Added proposal

2008-12-03T07:36:34Z

Added proposal

← Older revision		Revision as of 07:36, 3 December 2008
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	Due to the noise generated by the voting procedure from the first election, the procedure needs to be reevaluated and a better system needs to be put in place for the next election.		Due to the noise generated by the voting procedure from the first election, the procedure needs to be reevaluated and a better system needs to be put in place for the next election.

			== Proposal: RRV ==
			=== Variables ===
			*<math>l</math>: number of voters
			*<math>m</math>: number of candidates
			*<math>n</math>: number of seats
			*<math>i</math>: index of voters (<math>1 \le i \le l</math>)
			*<math>j</math>: index of candidates (<math>1 \le j \le m</math>)
			*<math>k</math>: index of seats (and rounds) (<math>1 \le k \le n</math>)
			=== Parameters ===
			A range for votes is selected by two limits, <math>a_{max}</math> and <math>a_{min}</math>.
			Reasonable choices include:
			*<math>a_{min}=0</math>, <math>a_{max}=1</math> (unbalanced, normalized)
			*<math>a_{min}=-1</math>, <math>a_{max}=1</math> (balanced)
			*<math>a_{min}=0</math>, <math>a_{max}=100</math> (unbalanced percentage; potentially useful if ratings were to be quantized)
			The effects of the voting system are generally independent of the limits selected, but a balanced range ''may'' be preferred by some voters to permit unknown candidates to be rated 0 with known, disliked candidates rated negative. Obviously this effect may be accomplished in an unbalanced range by rating unknown candidates <math>\tfrac{a_{min} + a_{max}}{2}</math>. Some calculations are simplified by using the unbalanced, normalized range, which makes it preferable from a numerical perspective.

			A ballot from voter <math>i</math> consists of <math>m</math> ratings <math>a_{ij}</math> for the <math>m</math> candidates, such that <math>a_{min} \le a_{ij} \le a_{max}</math>.

			=== Procedure ===
			After all ballots are collected, <math>n</math> rounds are held to choose the winners <math>w_{k}</math>, with one winner chosen per round. In the first round, the weighted ratings for each voter are initialized as <math>b_{ij1}=a_{ij}</math>. The weighted scores in each round are summed:

			<math>B_{jk}=\sum_{i=1}^{l}b_{ijk}</math>

			The highest-scoring candidate not yet elected wins; this is not simple to express formally:

			<math>w_k = \max ( B_{jk} \ni j \notin w_{1 \cdots k-1})</math>

			The weighted scores for each succeeding round are calculated by de-emphasizing ballots according to the portion in which they've already won:

			<math>b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}-a_{min}}{a_{max}-a_{min}}}</math>

			In the case of an unbalanced range (<math>a_{min} = 0</math>), <math>b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}}{a_{max}}}</math>, and in the normalized case (<math>a_{max} = 1</math>), <math>b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}a_{iw_p}}</math>.

	== Discussions ==		== Discussions ==

imported_>generalantilles at 18:42, 5 November 2008

2008-11-05T18:42:14Z

← Older revision		Revision as of 18:42, 5 November 2008
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	{{task\|~~proposed~~}}		{{task\|ongoing}}


	Due to the noise generated by the voting procedure from the first election, the procedure needs to be reevaluated and a better system needs to be put in place for the next election.		Due to the noise generated by the voting procedure from the first election, the procedure needs to be reevaluated and a better system needs to be put in place for the next election.


	== Discussions ==		== Discussions ==

imported_>generalantilles: /* Discussions */

2008-11-04T19:05:12Z

Discussions

← Older revision		Revision as of 19:05, 4 November 2008
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	== Discussions ==		== Discussions ==

	* [http://www.internettablettalk.com/forums/showthread.php?p=239338\|Defining the Maemo Community Council voting procedure - Internet Tablet Talk]		* [http://www.internettablettalk.com/forums/showthread.php?p=239338 Defining the Maemo Community Council voting procedure - Internet Tablet Talk]

	[[Category:Community]]		[[Category:Community]]
	[[Category:maemo.org]]		[[Category:maemo.org]]
	[[Category:Council]]		[[Category:Council]]