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 <[EMAIL PROTECTED]> 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.
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