Kristofer,

I, too, find myself going back to the risk-neutral lottery-based definition
of utility. I feel like it goes so naturally with "random ballot".

Suppose V1 has a ranking of A > B > C and V2 has a ranking of C > B > A. In
random ballot, V1's vote becomes a lottery ticket that causes A to win and
V2's vote becomes a lottery ticket that causes C to win. Let us ask when
would V1 and V2 both agree to trade their "one chance of A winning and one
chance of C winning" for "two chances of B winning".

We know we can say little about the "absolute" or "interpersonal" utilities
of how U_V1(A), U_V1(B), and U_V1(C) compare to U_V2(A), U_V2(B), and
U_V2(C).

But asking each voter to quantify exactly where B lies on the spectrum
between A and C, as a number between 0 and 1, is completely meaningful (in
the risk-neutral lottery paradigm).

Let b_1 = (U_V1(B) - U_V1(C)) / (U_V1(A) - U_V1(C))

Let b_2 = (U_V2(B) - U_V2(A)) / (U_V2(C) - U_V2(A))

(In other words, rescale each voter's utility so their favorite candidate
is at 1.0 and their least favorite is at 0.0 and examine their utility
estimations of B.)

If b_1 = 0.5 and b_2 = 0.5, we propose they trade "one chance of A winning
and one chance of C winning" for "two chances of B winning". The voters are
actually completely neutral toward this trade, though as an outsider I much
prefer the lowered entropy. b_1 and b_2 would have to be strictly greater
than 0.5 for both voters to be excited about the transaction.

It works for other fractions, too. If b_1 = 0.6 and b_2 = 0.4, the
utility-neutral trade is "one chance of A winning and one chance of C
winning" for "1.666 chances of B winning and 0.333 chance of C winning".
(If b_1 > 0.6 and b_2 > 0.4, then the trade is positive-sum.)

Can we actually set up this market (declared-strategy style), let all
voters submit their three-candidate ranking and a utility (between 0 and 1)
for their middle candidate, then we simulate all the trades and come up
with a final, optimal lottery?

A > B > C voters and C > B > A voters would trade with each other. A > C >
B voters and B > C > A voters would trade with each other. B > A > C voters
and C > A > B voters would trade with each other.

It seems obvious to me that in an election where 50% of the voters want A >
B > C and 50% want C > B > A, if you can get a number from each voter on
where B is on their scale from 0 to 1, that information is useful AND
meaningful. I mean, if all the voters say 0.9 then clearly we should just
elect B as the compromise candidate. And if all the voters say 0.1, then
giving them a 50/50 lottery between A and C is probably the best we can do.
Why should we decline to collect and use this "utility of the middle
candidate" information?

How can we simulate those trades? Line up all the A > B > C voters in order
of decreasing "B" utility and line up all the C > B > A voters in order of
increasing "B" utility and match up the two lines somehow? What about the
mismatch in length?

One problem I see is that whenever a transaction is perfectly fair, it is
utility-neutral, and the two parties are indifferent to whether the trade
actually happens. A trade that is positive-sum, on the other hand, has some
surplus utility and we could be unfair about which voter captures it.

If b_1 = b_2 = 0.6, then trading "one chance of A and one chance of C" for
any of the following would be utility-neutral or -positive for both voters:

• 1.666 chances of B winning and 0.333 chance of C winning
• 2 chances of B winning
• 1.666 chances of B winning and 0.333 chance of A winning

Obviously, as neutral election administrators, we should choose the middle
option. But I think this illustrates the opportunity for strategic voting
in this system. If you, as a voter, have perfect information about the
other voters, maybe your utility for B is 0.6 and you see that you can
decrease your declared utility for B to 0.400001 and still get a trade. It
will be a trade the other person barely agrees to, and you'll maximize your
utility, capturing all the surplus from the transaction.

Is there something else we could do as election administrators to make
dishonesty less profitable? Does it depend on the way we line up and match
up the opposing voters? If we always try to make sure that we match up
voters with a "sum of compromise utility" that is greater than one but as
small as possible, does that help somehow?

Perhaps in a large election, it will be difficult to know enough
information about the other voters and the benefits will be small enough
that voters will just be honest?

Or maybe we just discard the concept of matching up individual voters, look
at all the data, and come up with a "market-clearing price" for turning A
and C chances into B chances? Does that fix anything, or just leave a lot
of positive-sum transactions unfulfilled?

Can it be generalized to more than three candidates?

~ Andy

On Sun, Aug 15, 2021 at 3:02 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

Here are some of my thoughts about determining sincere ratiings with the
help of sincere rankings ... ratings adequate for use in lottery methods:

We set up a system of equations (to be solved iteratively) whose solutions
are the desired ratings.

First assign Top and Bottom ranked (or truncated) candidates the respective
boundary values of 100 and zero percent.

Each remaining candidate Y is interior to the ranks, i.e. ranked between
two neighbors X and Z. We use the lower case variables x, y, and z to
represent the ratings (whether given or to be determined) of the respective
candidates X, Y, and Z.

For each interior Y adjust parameters p and q (while keeping p + q = 100%)
interactively until the user is indifferent between the lotteries pX + qZ
and 100%Y, where X and Z are adjacent to Y in the ranking.

Then set y = px + qz .

Having done this for each interior Y, we now have a system of equations

{y = px+qa | Y is ranked consecutively between X and Z}

which together with the previously mentioned boundary conditions are
sufficient to uniquely determine the desired ratings.

In fact, an approximate solution set for this system can be obtained by
initializing all of the interior variables randomly and then iterating the
set of equations (always respecting boundary conditions) until the
variables converge (e.g.) to the accuracy of the math coprocessor, ... as
long as you realize the accuracy of the actual ratings cannot exceed the
accuracy of the p and q estimates provided by the user ... GIGO.

The main purpose of the above verbiage is to show that there is a
conceptually rigorous way to define meaningful ratings adequate for use in
lottery methods without mention of "utilities."

That said, forty plus years of assigning partial credit to student work has
taught me some useful shortcuts.

A problem that can be solved in n sinificant steps gets fraction k/n
partial credit if the student successfully completes k steps before getting
derailed.

Similarly, a candidate gets rating k/n if she meets k out of your n equally
important criteria. If not equally important, then includes weights.

Sometimes the easiest way to assign partial credit is to ask yourself the
question, "What is the probability that this student would successfully
solve a typical problem of this kind on another similar test?"

Similarly, you can ask what is the probability that this candidate would
faithfully represent your position on issues of importance to you (weighted
by importance)?

List the candidates in order of these weighted probabilities, then subtract
the smallest from all of them .... finally divide the resulting values by
the largest of these.  Note, however, that these normalization steps form
an affine transformation so they are not necessary if your lottery method
is invariant under affine transformations of the ballot ratings ... an
indispensable requirement for a decent lottery method.

I promise to show how to use these ratings ballots to make a lottery based,
but completely deterministic, party list proportional representation method.

How can that be?

Here's the trick: the alternatives of the lottery method are the party
lists themselves. Voters rate the lists rather than the separate candidates
within the lists. Then the number of candidates contributed by a list is N
times p, where p is the lottery probability of that list and where N is the
number of seats to be filled by the election.

If the lottery method is "random favorite party," then you get a basic
party list method depending on how you round the N*p values to whole
numbers.  Note that this method is absolutely deterministic despite its use
of lottery language to describe the distribution of winning candidates
among the various party lists.

But other proportional lottery methods (besides the benchmark
random-favorite lottery) with significantly lower entropy can lead to less
fragmentation and more potential for cooperation, without sacrificing
proportional representation of minority groups.

To be continued ...

FWS

El dom., 26 de sep. de 2021 11:44 p. m., Andy Jennings <
elections@jenningsstory.com> escribió:

On 9/27/21 8:43 AM, Andy Jennings wrote:

There are two threads to this that I think it's useful to keep separate.
The first is that since we're dealing with lotteries (over candidate
alternatives), it makes sense to consider actual lotteries
(probabilities of winning) based on this information. The second is
that, while interpersonal comparisons of utility are very hard (if not
impossible, e.g. qualia problems), we can access risk neutral lottery
information.

I was investigating the second aspect, because if Range and Approval's
failings come from asking more than the voter can provide (namely,
asking for utilities on an interval scale, and sort of just throwing its
hands in the air and say "then just normalize"), then it's natural to
ask, well, what kind of cardinal utility information can we get? And
how can a (deterministic) method that's honest about the limits to its
information be constructed?

The two threads or lines of investigation may be related, e.g. one such
method may be "determinize a random method by electing the candidate
with the greatest probability of victory", justified by arguing that
this will generally be a good candidate due to the linearity of
expectation. However, I would imagine that a method specifically
designed for the deterministic case would be better.

While it's also possible to e.g. take lottery information and "just
normalize", I have the impression that doing so would add information
that doesn't exist: it in a sense pretends that what isn't on an
interval scale actually is. It needs additional justification, e.g. that
OMOV means that each voter's power should the same, and that a voter
with an extreme preferences should have all his other preferences
diminuated rather than the scale being clamped.

Ordinary incommensurability would mean that you can only get an affine
scaling of the utilities (defined by the lotteries). But I was thinking:
at least for sensory (hedonic) types of utilitarianism, couldn't you
define a zero point by saying everything with utility less than zero is
something you'd prefer not to experience (i.e. you wouldn't prefer a
presence of this to an absence of this), while everything with utility
greater than zero is something you would?

Yes. I used a four-tuple because I was thinking "what if A and C are the
same utility value, then you'd get a division by zero". But if we also
gather honest rank information, that problem more or less goes away,
because it's clear who the voter's favorite and least favorite are
(excepting the degenerate case where the voter equal-ranks everybody).

There may still be numerical imprecision problems, but let's leave that
for now; no need to make it any more complex than it needs to.

So the sufficient data would seem to be: an ordering of c candidates,
plus (c-2) scale values. There are c-2 of these because in a
two-candidate election, there's no meaningful ratio between the favorite
and the least favorite, as the affine (or even linear) scaling make
their utilities completely ambiguous. All we know is that the favorite
is better than the least favorite.

But that this is sufficient suggests (at least at first glance) that
cyclical preferences may occur. And perhaps this is a natural
consequence of being limited to affine/linear scalings of utilities. I'd
have to think more about what such a cycle "means": I would guess it's
something like that any candidate in the cycle can win depending on what
the affine constants are (as opposed to say, a Pareto-domination
situation where everybody ranks A>B>C so that whatever the voters'
constants are, A is a better candidate than B).

I think the best approach in such a case would be to consider the method
as an optimization problem: then trading should result in much less path
dependence because the solver can consider the problem globally.

This optimization problem would contain a penalty on entropy, but I'm
not sure what more. The obvious choice would be to maximize social
utility, but since we only have affine transformations (or linear,
depending on whether the natural zero idea is tenable), we can't extract
social utility from the ballots, so I'm not sure how to do that.

(Well, you could fit a function of the ballots to maximize VSE under
say, a spatial model. But I'm not sure what such a function would look
like and if it would be generalizable. It sounds a bit ugly an approach.)

I'd think the trade idea would produce constraints on the allowed
solutions that we're optimizing over. Suppose that a A>B>C voter trades
with a C>B>A voter to decrease both the chance of A and C winning and
increase the chance of B winning. Then there exists a point where the
A>B>C voter has given up enough probability that any further increase in
B's chance of winning only lowers that voter's expected utility. At that
point, the voter is indifferent between an epsilon more of B winning,
and e/2 more of A and C winning. So that's a marginal constraint.

I'm not sure how the optimization method should find out who each voter
would consider trading with, though, and how to handle more complex
trades. In a market, that's usually handled through some kind of money,
but there's no money here. Someone who's better than me at
microeconomics could probably figure that out.

(But the good news, I think, is that the marginal constraints only need
the lottery information, because they're about indifference between two
lotteries.)

Yes, all of the above remarks are in the context of a honest system. The
deterministic system that I'm interested in would be subject to
Gibbard's earlier theorem, and the lottery method would probably be
subject to the later one.

I'm not sure if accounting for strategy can be done as easily through
the optimization framework. I think there are fields of study on this,
from an economic perspective, on how to add constraints that make
certain types of strategy pointless (at the expense of producing some
lower utility solution), but I don't know anything about them.

There's the generalized SARVO approach: arrange the voters in some
random order. The first voter goes first, the second voter optimizes his
vote given the first's ballot; the third optimizes wrt the two who went
before, and so on. Suppose the inner method returns a lottery. Choose
the lottery that is the expectation of all these lotteries. More complex
methods could try to use the minmax game AI algorithm for optimizing the
ballots. (The idea for both is related to the concept of "averaging over
clairvoyance", which is used in imperfect information game AI when there
are no information-gathering moves.)

But your idea might be both simpler to program and more comprehensible.
For a deterministic method, if you can get enough voters to compromise,
it doesn't matter if the other voters strategize away from the
compromise, because the compromise candidate will win anyway. So first
choosing voters who have the most to gain by compromising but not so
much that they could've misrepresented their ballots (by strategy) and
got a better result, might work.

Other ideas: perhaps there is some kind of Condorcet analog, i.e.
treating the ranks plus (n-2) factors as biasing the preferences. If so,
we could then use standard Condorcet methods on the result and get
something that's "majoritarian by utility" -- although it wouldn't
exactly be by utility, since the factors don't set utility. But perhaps
one could prove say, that if there's a lottery that involves only some
candidates, and everybody (or some large enough fraction by strength of
preference) prefers every lottery containing only candidates in that set
to lotteries containing everybody, then that set (an analog of the Smith
set) should win.

Forest,

Thanks for your thoughts.

I agree that there are many good ways to get cardinal information from
voters on a valid interval scale, assuming that we don't try to compare
intervals between voters. It seems that the cardinal information must be
meaningful and it's a shame to throw it away (though I agree that the
method should be invariant to affine transformations).

Speaking of lottery methods, it's interesting that there is so much
reluctance (including my gut reaction) to actually recommend a
lottery-based method for use in real political elections. We want our
elections to be deterministic, not influenced by chance in any way. But
certainly there is chance in the process. Weather can influence turnout, as
can traffic. There may be some voters that actually flip a coin in the
voting booth. Cosmic rays have affected vote counts in the past (
https://youtu.be/AaZ_RSt0KP8?t=44). Websites like FiveThirtyEight report on
the whole election season with probabilities. And sitting there watching
outcomes on election night can definitely feel like
games-of-chance-and-skill like the Olympics.

So maybe we should just embrace it and try to convince people to use
lottery methods.

Even if we trust the math that generates the lottery, maybe we just can't
bring ourselves to believe that the final draw will not be rigged. I'm sure
there are cryptographic methods for securely generating a random number
between 0 and 1, but will the public trust them?

Is the NIST randomness beacon trustworthy?

In a small enough election, you could agree to use randomness from the next
block mined on the bitcoin blockchain, but that runs into problems at the
scale of a national election.

~ Andy

On Thu, Sep 30, 2021 at 9:51 PM Forest Simmons forest.simmons21@gmail.com
wrote:

Kristofer,

Thank you for thinking this over.

I do think the concept of an absolute zero (things I would like to
experience vs things I wouldn't) has some merit. Maybe if we were deciding
where to go to dinner, there would be some places I would just not go. The
company of my friends wouldn't be worth the pain of the venue. But in a
political election, it's harder to imagine where the absolute zero would
fall.

Here are some thoughts about facilitating the market:

Suppose there are N_A voters who want A > B > C and N_C voters who want C >
B > A. Assume all voters also submitted an evaluation of B (a real number
in [0,1]).

Find all the integer ordered pairs (a, c) in [1, N_A] x [1, N_C] such that
there is an a-sized subset of the A>B>C voters and a c-sized subset of the
C>B>A voters that are willing to, collectively, trade their chances of A
and C winning for chances of B winning. The subsets will not be difficult
to find. They will be the subsets of the A>B>C and C>B>A voters with the
highest opinion of B.

For each (a,c), we can simply ask whether both of the following are true:

a / (a + c) <= a-th highest evaluation of B by A>B>C voters
c / (a + c) <= c-th highest evaluation of B by C>B>A voters

We can solve the first one for c as an increasing function of a, and the
second one for a as an increasing function of c and see where they overlap.
Since they are increasing, there is always a maximal pair (a,c).

Here is an example:

Suppose there are 13 A>B>C voters with the following evaluations of B:
0.1, 0.25, 0.3, 0.3, 0.4, 0.45, 0.5, 0.5, 0.57, 0.571, 0.9, 0.9, 0.95

And 7 C>B>A voters with the following evaluations of B:
0.1, 0.1, 0.4, 0.5, 0.5, 0.65, 0.95

The 1 most-willing A>B>C voter (0.95) would trade with (0.05/0.95) = 0.053
(or more) C>B>A voters.
The 2 most-willing A>B>C voters (0.9+) would trade with 2*(0.1/0.9) =
0.222+ C>B>A voters.
The 3 most-willing A>B>C voters (0.9+) would trade with 3*(0.1/0.9) =
0.333+ C>B>A voters.
The 4 most-willing A>B>C voters (0.571+) would trade with 4*(0.429/0.571) =
3.005+ C>B>A voters.
The 5 most-willing A>B>C voters (0.57+) would trade with 5*(0.43/0.57) =
3.772+ C>B>A voters.
The 6 most-willing A>B>C voters (0.5+) would trade with 6*(0.5/0.5) = 6+
C>B>A voters.
The 7 most-willing A>B>C voters (0.5+) would trade with 7*(0.5/0.5) = 7+
C>B>A voters.
The 8 most-willing A>B>C voters (0.45+) would trade with 8*(0.55/0.45) =
9.778+ C>B>A voters.
The 9 most-willing A>B>C voters (0.4+) would trade with 9*(0.6/0.4) = 13.5+
C>B>A voters.
The 10 most-willing A>B>C voters (0.3+) would trade with 10*(0.7/0.3) =
23.333+ C>B>A voters.
The 11 most-willing A>B>C voters (0.3+) would trade with 11*(0.7/0.3) =
25.667+ C>B>A voters.
The 12 most-willing A>B>C voters (0.25+) would trade with 12*(0.75/0.25) =
36+ C>B>A voters.
All 13 A>B>C voters (0.1+) would trade with 13*(0.9/0.1) = 117+ C>B>A
voters.

The 1 most-willing C>B>A voter (0.95) would trade with (0.05/0.95) = 0.053+
A>B>C voters.
The 2 most-willing C>B>A voters (0.65+) would trade with 2*(0.35/0.65) =
1.077+ A>B>C voters.
The 3 most-willing C>B>A voters (0.46+) would trade with 3*(0.5/0.5) = 3+
A>B>C voters.
The 4 most-willing C>B>A voters (0.45+) would trade with 4*(0.5/0.5) = 4+
A>B>C voters.
The 5 most-willing C>B>A voters (0.4+) would trade with 5*(0.6/0.4) = 7.5+
A>B>C voters.
The 6 most-willing C>B>A voters (0.1+) would trade with 6*(0.9/0.1) = 54+
A>B>C voters.
All 7 C>B>A voters (0.1+) would trade with 7*(0.9/0.1) = 63+ C>B>A voters.

The (a, c) ordered pairs of successful trades are:
(1,1)
(2,1)
(3,1)
(2,2)
(3,2)
(3,3)
(4,4)
(5,4)

So we implement the maximal trade, 5 chances of A winning and 4 chances of
C winning turn into 9 chances of B winning. Our lottery goes from:
13/20 A + 7/20 C
to:
8/20 A + 9/20 B + 3/20 C

Is there a better definition of "market-clearing price"?

However, this does not seem to lower the entropy, like I expected. Entropy
must not be what I'm looking for.

The thing I like about this (similar to the strategy-proof aggregation
functions like the median or chiastic median) is that what ended up
mattering is that there were 5 A voters who graded B at or above 0.555 and
4 C voters who graded B at or above 0.444. The actual grades didn't matter
beyond that, so small adjustments by most voters won't change the outcome
at all. Yes, there are a few voters at the margin who could affect the deal
by going above or below the threshold, but in general, this system should
have some good strategy-resistance properties.

Of course, with perfect knowledge, one A voter might notice that a little
dishonesty (real utility=0.57, professed utility=0.55) will eliminate the
(5,4) trade and leave the (4,4) trade. They still get the same number of C
voters (4) converted to B voters, but it only costs them 4 A voters instead
of 5. They could have captured some of the surplus utility and kept it for
themselves.

This method is vulnerable because it's not making all trades at the
individual level. It doesn't really care that every trade at the margin is
net-positive-utility. It seems to use the surplus utility of the
most-willing-to-trade voters to get more people in on the deal at the
margin.

On the other hand, if one of the C voters thought they might benefit from
dishonesty and professed utility 0.44 (real utility=0.5), they would
scuttle both the (5,4) trade and the (4,4) trade, leaving (3,3) as the best
trade. This effectively causes 2 A votes and 1 C vote to NOT get traded for
3 B votes, a net-negative utility for them.

So hopefully it is only possible for a few voters (right at the margin) to
affect the outcome at all and hopefully it will be impossible to tell,
before the election, if being dishonest will help you or hurt you.

Thoughts?

~ Andy

On Sun, Oct 3, 2021 at 4:39 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 05.10.2021 04:54, Andy Jennings wrote:

If lotteries are on the table, then perhaps we should just dissolve the
electoral problem and go right to sortition. It certainly has appealing
corruption resistance properties :-)

But the problem of lotteries, I think, is that there's too much left to
chance. While every election leaves something to chance (as you've
correctly pointed out), it's not too much to destabilize the process. On
the other hand, if you have the simple random favorite lottery and 10%
of the voters vote for a dictator, then you have 10% chance of getting a
dictatorship.

One way of considering single-winner methods, I think, is that they try
to find the best outcome under the constraint of zero entropy.
Proportional representation methods might also need to compromise to
satisfy their seat limits. Perhaps it would be possible to create a
tunable entropy method where we set a maximum allowed entropy (or
variance), and it attempts to find the best outcome lottery subject to
this constraint. Such a constraint would help with the reluctance, I
think, as long as the threshold is set sufficiently low that there's no
chance of extreme upsets (like a dictator winning).

There was a thread about this on Reddit a while ago. There's a protocol
that goes like this:

Somehow pick a number of participants (they may be the whole electorate
or randomly chosen members of the public, or the representatives of the
previous term).

Each participant creates a sufficiently long random secret string and
publishes its cryptographic hash.

The participants (or the election officials) publish these hashes.

Once they're all published, each participant reveals his random string.
If they match their respective hashes, the strings are combined, and the
result is used as a seed for a CSPRNG.

This protocol works by forcing the participants to commit to their input
strings before they have any knowledge of the other strings. Thus they
can't adapt the inputs to fix a particular output.

Suppose there's a conspiracy to fix the output by bribing or coercing
the participants into selecting predetermined random strings. Then even
if a single member defects from the conspiracy, the chaotic nature of
the secure hash function makes the attack fail. If the combination
function is secure (e.g. a secure hash), then a conspiracy would in any
case have to use brute force to find a suitable set of strings. The
difficulty of this brute-forcing would depend on the entropy - e.g.
packing a majority of a sortition assembly of 100 would be prohibitive,
but changing the outcome of an election lottery with a few candidates
would be easier.

There have been proposals to use public data as entropy sources, e.g.
this one for financial data:
https://www.usenix.org/legacy/event/evtwote10/tech/full_papers/Clark.pdf

If multiple countries were to provide signed public randomness beacons,
they could be used as part of the protocol above; every country would
have to be collaborating to force the output. Number stations would
almost work, except they aren't signed.

-km

Dear All,

But Elections are a statistic -- a sum of contingent choices. Votes are not in a logical relation to each other, such that there is some determinable right answer to who should be elected. Axiomatic deduction of a deterministic result is the reason why the Impossibility theorem is impossible -- it is a misconception of the nature of elections.

We can make probabilistic determinations of electing candidates, ranging from practically certain to completely indecisive. The most representative results depend on most representatively averaging the preference data. This avoids the usual social choice theory objections, that assume elections are analytic rather than synthetic.

Regards,
Richard Lung.

On 5 Oct 2021, at 10:46 pm, Kristofer Munsterhjelm km_elmet@t-online.de wrote:

If lotteries are on the table, then perhaps we should just dissolve the
electoral problem and go right to sortition. It certainly has appealing
corruption resistance properties :-)

But the problem of lotteries, I think, is that there's too much left to
chance. While every election leaves something to chance (as you've
correctly pointed out), it's not too much to destabilize the process. On
the other hand, if you have the simple random favorite lottery and 10%
of the voters vote for a dictator, then you have 10% chance of getting a
dictatorship.

One way of considering single-winner methods, I think, is that they try
to find the best outcome under the constraint of zero entropy.
Proportional representation methods might also need to compromise to
satisfy their seat limits. Perhaps it would be possible to create a
tunable entropy method where we set a maximum allowed entropy (or
variance), and it attempts to find the best outcome lottery subject to
this constraint. Such a constraint would help with the reluctance, I
think, as long as the threshold is set sufficiently low that there's no
chance of extreme upsets (like a dictator winning).

There was a thread about this on Reddit a while ago. There's a protocol
that goes like this:

Somehow pick a number of participants (they may be the whole electorate
or randomly chosen members of the public, or the representatives of the
previous term).

Each participant creates a sufficiently long random secret string and
publishes its cryptographic hash.

The participants (or the election officials) publish these hashes.

Once they're all published, each participant reveals his random string.
If they match their respective hashes, the strings are combined, and the
result is used as a seed for a CSPRNG.

This protocol works by forcing the participants to commit to their input
strings before they have any knowledge of the other strings. Thus they
can't adapt the inputs to fix a particular output.

Suppose there's a conspiracy to fix the output by bribing or coercing
the participants into selecting predetermined random strings. Then even
if a single member defects from the conspiracy, the chaotic nature of
the secure hash function makes the attack fail. If the combination
function is secure (e.g. a secure hash), then a conspiracy would in any
case have to use brute force to find a suitable set of strings. The
difficulty of this brute-forcing would depend on the entropy - e.g.
packing a majority of a sortition assembly of 100 would be prohibitive,
but changing the outcome of an election lottery with a few candidates
would be easier.

There have been proposals to use public data as entropy sources, e.g.
this one for financial data:
https://www.usenix.org/legacy/event/evtwote10/tech/full_papers/Clark.pdf

If multiple countries were to provide signed public randomness beacons,
they could be used as part of the protocol above; every country would
have to be collaborating to force the output. Number stations would
almost work, except they aren't signed.

-km

Election-Methods mailing list - see https://electorama.com/em for list info

Richard,

Thanks for stimulating my imagination!

Forest

El mar., 5 de oct. de 2021 4:38 p. m., Richard Lung voting@ukscientists.com
escribió: