[EM] Some chance for consensus revisited: Most simple solution
Jobst Heitzig
heitzig-j at web.de
Sun Feb 1 13:02:02 PST 2009
Dear folks,
I want to describe the most simple solution to the problem of how to
make sure option C is elected in the following situation:
a% having true utilities A(100) > C(alpha) > B(0),
b% having true utilities B(100) > C(beta) > A(0).
with a+b=100 and a*alpha + b*beta > max(a,b)*100.
(The latter condition means C has the largest total utility.)
The ultimately most simple solution to this problem seems to be this method:
Simple Efficient Consensus (SEC):
=================================
1. Each voter casts two plurality-style ballots:
A "consensus ballot" which she puts into the "consensus urn",
and a "favourite ballot" put into the "favourites urn".
2. If all ballots in the "consensus urn" have the same option ticked,
that option wins.
3. Otherwise, a ballot drawn at random from the "favourites urn"
decides.
Please share your thoughts on this!
Yours, Jobst
Jobst Heitzig schrieb:
> Hello folks,
>
> I know I have to write another concise exposition to the recent
> non-deterministic methods I promote, in particular FAWRB and D2MAC.
>
> Let me do this from another angle than before: from the angly of
> reaching consensus. We will see how chance processes can
> help overcome the flaws of consensus decision making.
>
> I will sketch a number of methods, give some pros and cons, starting
> with consensus decision making.
>
> Contents:
> 1. Consensus decision making
> 2. Consensus or Random Ballot
> 3. Approved-by-all or Random Ballot
> 4. Favourite or Approval Winner Random Ballot: 2-ballot-FAWRB
> 5. Calibrated FAWRB
> 6. 4-slot-FAWRB
> 7. 5-slot-FAWRB
>
>
>
> 1. Consensus decision making
> ----------------------------
> The group gathers together and tries to find an option which everyone
> can agree with. If they fail (within some given timeframe, say), the
> status quo option prevails.
>
> Pros: Ideally, this method takes everybody's preferences into account,
> whether the person is in a majority or a minority.
>
> Cons: (a) In practice, those who favour the status quo have 100% power
> since they can simply block any consensus. (b) Also, there are problems
> with different degrees of eloquence and with all kinds of group-think.
> (c) Finally, the method is time-consuming, and hardly applicable in
> large groups or when secrecy is desired.
>
>
> Let us address problem (a) first by replacing the status quo with a
> Random Ballot lottery:
>
>
> 2. Consensus or Random Ballot
> -----------------------------
> Everybody writes her favourite option on a ballot and gives it into an
> urn. The ballots are counted and put back into the urn. The number of
> ballots for each option is written onto a board. The group then tries to
> find an option which everyone can agree with. If they fail within some
> given timeframe, one ballot is drawn at random from the urn and the
> option on that ballot wins.
>
> Pros: Since the status quo has no longer a special meanining in the
> process, its supporters cannot get it by simply blocking any consensus -
> they would only get the Random Ballot result then. If there is exactly
> one compromise which everybody likes better than the Random Ballot
> lottery, they will all agree to that option and thus reach a good
> consensus.
>
> Cons: Problems (b) and (c) from above remain. (d) Moreover, it is not
> clear whether the group will reach a consensus when there are more than
> one compromise options which everybody likes better than the Random
> Ballot lottery. (e) A single voter can still block the consensus, so the
> method is not very stable yet.
>
>
> Next, we will address issues (b), (c) and (d) by introducing an approval
> component:
>
>
> 3. Approved-by-all or Random Ballot
> -----------------------------------
> Each voter marks one option as "favourite" and any number of options as
> "also approved" on her ballot. If some option is marked either favourite
> or also approved on all ballots, that option is considered the
> "consensus" and wins. Otherwise, one ballot is drawn at random and the
> option marked "favourite" on that ballot wins.
>
> Pros: This is quick, secret, scales well, and reduces problems related
> to group-think. A voter has still full control over an equal share of
> the winning probability by bullet-voting (=not mark any options as "also
> approved").
>
> Cons: (b') Because of group-think, some voters might abstain from using
> their bullet-vote power and "also approve" of options they consider
> well-supported even when they personally don't like them better than the
> Random Ballot lottery. Also, (e) from above remains a problem, in
> particular it is not very likely in larger groups that some options is
> really approved by everyone.
>
>
> Now comes the hardest part: Solving problems (b') and (e) by no longer
> requiring full approval in order to make it possible to reach "almost
> unanimous consensus" when full consensus is not possible. In doing so,
> we must make sure not to give a subgroup of the electorate full power,
> so that they can simply overrule the rest. Instead, we must make the
> modification so that still every voter has full control over an equal
> share of the winning probability. This is why we cannot just lower the
> threshold for consensus from 100% to, say, 90%. What we do instead is this:
>
>
> 4. Favourite or Approval Winner Random Ballot (FAWRB),
> simplest version, using two ballots (2-ballot-FAWRB)
> -------------------------------------------------------
> Still, each voter marks one option as "favourite" and any number of
> options as "also approved" on her ballot. The option getting the largest
> number of "favourite" or "also approved" marks is nominated as
> "compromise". Two ballots are drawn at random. If the nominated
> compromise is marked on both as "favourite" or "also approved", it wins.
> Otherwise, the option marked as "favourite" on the first of the two
> ballots wins.
>
> Pros: Full consensus can be reached if some option is approved by
> everyone. Such an option will win with certainty. If no such option
> exists, also partial consensus can be reached: if, say, 90% agree to the
> best compromise option, that option will win with at least 81%
> probability (=90%*90%). On the other hand, bullet-voting still assures
> that my favourite gets my share of the winning probability: if 5%
> bullet-vote, their favourite gets at least 5% of the winning
> probability. Problem (b') shall no longer exist since by not approving I
> do not destroy the consensus complete but only lower the compromise's
> probability a bit.
>
> Cons: (f) The incentive to approve a good compromise is only there when
> I prefer the compromise quite a lot to the Random Ballot lottery, not
> when I prefer it only slighty. (g) If the process of nominating options
> does not prevent this, there is the possibility that a really harmful
> option is elected with some small probability.
>
>
> (Another method which achieves almost the same as 2-ballot-FAWRB is the
> older D2MAC which is very similar.)
>
>
> The game-theoretic reason for problem (f) is this:
>
> Consider a situation in which C is the compromise and all N voters
> approve it (N being large for simplicity). Now consider that I ask
> myself whether it would server my better not to approve C but to
> bullet-voter for my favourite, A. If I remove my approval for C, the
> winning probabilities change in the following way: C no longer wins with
> probability 1 but only with approximately probability 1 - 2/N (more
> precisely 1 - 2/N + 1/N²). My favourite A's winning probability grows
> from 0 to 1/N, since A now wins whenever my ballot is the first of
> the two drawn ballots. But at the same time, also the other voters'
> favourites' winning probabilities grow, since another voter's favourite
> now wins when my ballot is the second drawn ballot. In other words, the
> probability of ending up with a Random Ballot lottery result grows from
> 0 to approximately 1/N, too. Therefore, bullet-voting only makes
> sense when the utility I assign to the compromise C is smaller than the
> mean of (i) the utility I assign to my favourite A and (ii) the utility
> I assign to a Random Ballot lottery. In other words, it is better to
> cooperate in the election of C only when I rate C higher than half the
> way up from my rating of the Random Ballot lottery to my favourite's
> rating.
>
>
> Important: Although the FAWRB process always uses a chance process,
> namely drawing ballots, it will still usually lead to a deterministic or
> almost deterministic result! This is because with the incentives in
> place, people are usually very good at finding compromises which they
> then will (almost) all approve of, giving them 100% (or almost 100%)
> winning probability! Just as in "Consensus or Random Ballot", the very
> fact that the voters don't like the Random Ballot lottery when a
> compromise exists will lead to the compromise being elected and the
> Random Ballot being avoided.
>
>
> The next step towards my recommended version of FAWRB reduces this
> problem (f) by replacing the fixed number of three ballots by a more
> sophisticated drawing process:
>
>
> 5. Favourite or Approval Winner Random Ballot,
> calibrated version, using 3 or 15 ballots (calibrated FAWRB)
> ---------------------------------------------------------------
> Still, each voter marks one option as "favourite" and any number of
> options as "also approved" on her ballot. The option getting the largest
> number of "favourite" or "also approved" marks is still nominated as
> "compromise". A die is tossed. If it shows a six then 15 ballots are
> drawn at random, otherwise only 3 ballots. If the nominated compromise
> is marked on all these ballots as "favourite" or "also approved", it
> wins. Otherwise, the option marked as "favourite" on the first of the
> drawn ballots wins.
>
> Pros: As in 2-ballot-FAWRB, but now voters will also approve compromises
> they only find slightly better than the Random Ballot lottery (more
> precisely: which they rate higher than 1/5 of the way up from their
> rating of the Random Ballot lottery to their favourite's rating).
>
> Cons: Problem (g) from above remains. (h) When there are more than one
> possible compromise options, say C1 and C2, some voters may apply
> "approval strategy" and refuse to approve of C1 in order to get C2
> nominated instead of C1. When C1 is nominated anyway, they thereby
> reduce C1's winning probability unnecessarily.
>
>
> Mathematical note: The reason why the mentioned "approval limit" moves
> from 1/2 down to 1/5 of the way from Random Ballot to favourite is that
> the expected number of ballots drawn moved from 2 to 5.
>
>
> Next, we tackle problem (h) by decoupling the nomination of the
> compromise from the later agreement to the nominated compromise. This
> can be achieved by simply splitting the "also approved" slot into two
> slots named "good compromise" (used for both nomination and agreement)
> and "agreeable" (used only for agreement):
>
>
> 6. Favourite or Approval Winner Random Ballot,
> version with four slots (4-slot-FAWRB)
> ----------------------------------------------
> Each voter marks one option as "favourite", any number of options as
> "good compromise" and any number of options as "agreeable" on her
> ballot, the unmarked options being implicitly regarded as "bad". The
> option getting the largest number of "favourite" or "good compromise"
> marks (but not counting "agreeable" marks!) is nominated as
> "compromise". A die is tossed. If it shows a six then 15 ballots are
> drawn at random, otherwise only 3 ballots. If the nominated compromise
> is marked on all these ballots as "favourite", "good compromise", or
> "agreeable", it wins. Otherwise, the option marked as "favourite" on the
> first of the drawn ballots wins.
>
> Pros: Voters can now use approval strategy for the nomination step
> without reducing the final winning probability of the nominated
> compromise: The can just give only some one of the potential compromise
> options the "good compromise" mark and giving the other acceptavle
> compromise options the "agreeable" mark.
>
> Cons: Only problem (g) might remain.
>
>
> The final step is only needed when there is the possibility that some
> really bad option can actually make it onto the ballot. It is not needed
> when options are first checked by some independent authority for their
> feasibility, as is often implicitly done in political systems by supreme
> courts or the like.
>
> So, if (g) is really a problem, we can try to reduce it by introducing
> some mechanism by which a really large majority (say, 90%) can
> prevent an option from being accepted on the ballot. This leads me to
> the final version of FAWRB:
>
>
> 7. Favourite or Approval Winner Random Ballot,
> version with supermajority-veto (5-slot-FAWRB)
> -------------------------------------------------
> Each voter marks one option as "favourite", any number of options as
> "good compromise", any number of options as "agreeable", and maybe some
> options as "harmful" on her ballot, the unmarked options being
> implicitly regarded as "bad". Every option receiving more than 90%
> "harmful" marks is removed before we continue as in 4-slot-FAWRB: Of the
> remaining options, the one getting the largest number of "favourite" or
> "good compromise" marks (but not counting "agreeable" marks!) is
> nominated as "compromise". A die is tossed. If it shows a six then 15
> ballots are drawn at random, otherwise only 3 ballots. If the nominated
> compromise is marked on all these ballots as "favourite", "good
> compromise", or "agreeable", it wins. Otherwise, the option marked as
> "favourite" on the first of the drawn ballots wins.
>
> Pros: The "harmful" slot allows a 90% majority to keep harmful extremist
> options from having a chance.
>
> Cons: This supermajority-veto can be used to oppress minorities which
> are smaller than 10%, because they have no longer full control over
> their share of the winning probability.
>
>
> Hopefully that explains some things.
> I will also put the definitions into the Electowiki within a few days.
>
> Yours, Jobst
>
>
> Raph Frank schrieb:
>> On Sat, Oct 25, 2008 at 8:02 PM, Greg Nisbet
>> <gregory.nisbet at gmail.com> wrote:
>>> Ok now the actual criticism. I know that FAWRB is nondeterministic.
>>> Here is why that is bad.
>>>
>>> Factions (both unwilling to compromise):
>>>
>>> A 55%
>>> B 45%
>>>
>>> you view A as gaining a "55% chance of victory".
>>>
>>> This reasoning is flawed. Instead of viewing A as getting .55 victory
>>> units, think of it as a random choice between two possible worlds:
>>>
>>> A-world and B-world
>>>
>>> A-world is 10% more likely to occur, however they share remarkable
>>> similarities.
>>>
>>> In both worlds >=45% of the people had no say whatsoever.
>>
>> The trick with his method is that neither A-world or B-world is likely
>> to actually occur. It creates an incentive to find a compromise,
>> called say, AB-world.
>>
>> If all voters vote reasonably, then the result is a high probability
>> that the AB option will be picked.
>>
>> The utlities might be
>> ..... A-AB-B
>> 55: 100-70-0
>> 45: 0-70-100
>>
>> In effect, each A supporter agrees to switch his probability to AB in
>> exchange for a B supporter switching to AB.
>>
>> So, the initial probabilities would be
>>
>> A: 55%
>> AB: 0%
>> B: 45%
>>
>> Expected utility
>> 55: 55
>> 45: 45
>> Total: 100
>>
>> However, after the negotiation stage, the results might be
>>
>> A: 10%
>> AB: 90%
>> B: 0%
>>
>> Expected utility
>>
>> 55: 10% of 100 and 90% of 70 = 73
>> 45: 90% of 70 = 63
>> Total: 136
>>
>> I don't 100% remember the method (and it could do with a web
>> description :p ), but that is what it is attempting to do.
>>
>> The idea is not that it is random. The idea is that it says "OK, if
>> you can't all agree on a compromise, then we will pick a winner at
>> random".
>>
>> The threat that a random winner will be picked is what allows the
>> negotiation. If a majority can just impose its will, then there is no
>> point in compromising.
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
More information about the Election-Methods
mailing list