(Currently complete, but subject to change with post—unless different versions are separate posts?)
Content:
Contents:
Content
Open
Addressed by document’s later contents
Style
(Numbering is within sections and only reflects order within text (appearance), but doesn’t cross categories.)
Open:
1.
In a statistical sense, that would mean the loss function would be something like: the expected squared difference between the percent a proposal gets in the legislature, and the percent it would have gotten in a direct referendum, given that the proposal is drawn from some predefined distribution over possible proposals.
I’m curious how this loss function differs from the results being the same, rather than the ratios. I’d guess that it would get smoother results, but the main issue would probably be interactions. (Systematic rather than random variance.)
Which brings us to the third way better outcomes might be possible: by making representatives accountable primarily not on a moment-by-moment basis, but on a once-per-election time cycle, we might nudge them to think from a slightly more future-oriented perspective.
The question of how to get a future oriented perspective seems an empirical one.
2.
For example, imagine the fictional planet mentioned in The Hitchhikers’ Guide to the Galaxy, where people vote to elect lizards. Though the complete lack of representativity makes this a poor democracy, it would clearly be even less democratic if the losing lizard committed electoral fraud.
Obligatory mention that gerrymandering might be detectable by measuring variance in outcomes (of elections).
If the “effective dimension” is low, then a relatively small legislature can do quite a good job at representing even an infinite population.
But the election would take forever.
If the effective dimension is high, though, then the ideological distance between a randomly-chosen voter and the closest member of the legislature, will tend to be almost as high as the distance between any two randomly-chosen voters. In other words, there will be so many ways for any two people to differ, that the very idea that one person could “represent” another well begins to break down (unless the size of the legislature grows exponentially in the number of effective dimensions)
Unless people are organized into groups based around a group that literally negotiate over the tradeoffs, possibly reversing the ‘usual’ direction of voters → legislature. With the last step being the one that makes the Laws.
3.
What is the effective dimension of political ideology in reality? It depends how you measure it. If you look at US incumbent politicians’ voting records using a methodology like DW-NOMINATE
The choice of dimensions seems like a bigger deal than the number.
But if I’m wrong, and the variation in political opinions/interests that are politically salient in an ideal world is much higher, then the very “republican idea” of representative democracy is problematic.
And the question of whether things (like the factors captured by the dimensions, as well as ‘representability’) interact with each other to greatly affect outcomes (laws or whatever the means in question is that itself leads to outcomes).
4.
Having individual representation, where each voter can point to the representative they helped elect, and each representative was elected by an equal number of voters, is good from several perspectives.
Why? Getting a more diverse set of perspectives seems doable via:
Electing one or more officials with different numbers of votes, but giving them power based on the number of votes they received. (Officials with less power may have less of an impact most of the time.* But if they’re able to bring new ideas to the table that work...)
*Ignoring the possibility of officials with powers based on circumstance, or within certain domains.
For instance, in this case, we could optimize for piety even while also ensuring unbiasedness and minimizing variance.
Variance seems like it might be a red herring, given a focus on outcomes/exemplariness.
5.
3a from the next section seems like it might be relevant.
In practice, it’s impossible to create a voting method that elects S equally-weighted candidates without wasting some votes; typically at least somewhere between 1/2S and 1/(S+1) of them.
Imprecision: instead of dividing voters into S separate groups with one representative per group, the method might divide them into fewer groups with more than one representative each. This almost certainly would lead to higher bias and/or variance at the next step.
Weird methods:
Representatives are chosen from Group A, but chosen by Group B voters. (There’s also changing power amounts as mentioned previously.)
6.
Note that in rating a voting method, we’re doing this “backwards”: we constructed the “set of responsible voters” from the candidate, not vice versa.
In some ways there seemed to be a similar circularity around the use for “utilitarianism” whcih seemed to mean ‘representativeness of democracy’ in context.
.… (I’m making good progress writing this but I’ve gotta go now; to be continued)
I look forward to seeing more in this section.
Addressed by document’s later contents:
1.
When you’re choosing between a finite number of options that are known at the time of voting, you need a single-winner voting method. It’s pretty easy to define a way to measure “how good” such a method is: we can just use utilitarianism.
utilitarianism
Based on the rest of this document, you mean a utility function*, or something else very different from utilitarianism.
This (later) part makes it more clear:
The legislative outcome is an approximation of the popular outcome which is an approximation of the ideal outcome; if the first step of approximating goes wrong, there’s no reason to believe the second step will fix it.
2.
But electing a legislature is something different. How do you define the utility of a legislature that has a 60⁄40 split between two parties, versus one that has 70⁄30 split?
Depends on the system—The utility is based on the actions of the legislature (and also it’s cost and thus size, especially if the people/voters have to pay for it).
(Later) Addressed here:
The legislative outcome is an approximation of the popular outcome which is an approximation of the ideal outcome; if the first step of approximating goes wrong, there’s no reason to believe the second step will fix it.
3.
In practice, “all” tends to be limited by some eligibility criteria, but I’d say that most such criteria make the system less democratic, other than maybe age and residency.
The normative case that this kind of democracy is a good idea tends to rest on the Condorcet jury theorem: that is, if the average voter is more likely to be “right” than “wrong” (for instance, more likely to choose the option which will maximize global utility), then the chances the referendum outcome will be “right” quickly converge towards 100% as the number of voters increases.
a) Voters could also be selected to ‘create/represent’ conflict, and see which side wins. (If the remaining population that hasn’t voted isn’t big enough to overturn the current win/result, the voting stops, or the result is passed. (An error rate/margin could also be included.))
b) This could be reversed; the voters are selected in order to create a body in which
the average voter is more likely to be “right” than “wrong”
and where additional voters improve this probability.
c)
which will maximize global utility
The question of cost is also a matter of global utility.
d)
If instead of voters voting, a body that deliberates on the question/s this can allow for more options being evaluated, and perhaps more “right” being found—though the bigger the body (and the search space), the longer this might take, and costs probably should be taken into account.
Later addressed here:
First, it may even be that there is some optimum size for reasoned debate and
(And it may be different for “exemplary representatives”.)
Style:
on a fooding
on a footing
((OK, “effective dimension” isn’t exactly that; it measures not only how many “relatively big” dimensions there are, but also how “relatively small” the rest are. I’m being deliberately vague about how precisely I’d define “effective dimension” because I suspect that unless you ignore variation below a certain noise threshold the ED is actually infinite in the limit of infinite voters.))
...
))(...)((
The multiple parenthesis are an interesting style choice.
The “ongoing” nature of this post is interesting and I like it. Having read it as it is, I think it worked really well, and some of the empty sections could fit together in a different post. Though since they don’t exist I don’t know how important the connections between them in one document are. (Maybe having this version as is might be useful.)
Key to strange punctuation I use: “((...))” are technical notes that you can safely skip if you don’t understand; the extra parens are to emphasize the skippability. ”))(...)((” are digressions that break the narrative flow, but are actually important; the inner normal parens are to mark digression and the doubled outer reverse parens are to mark importance.
Also I wrote TLD̦R instead of TL;DR (too long; didn’t read) because on my keyboard the semicolon is a dead key that combines with space or enter to be an ordinary semicolon but combines with letters to add accents. I think making TLD̦R one character shorter is in the spirit of TL;DR.
I’ve switched over to responding to your comments/suggestions one-by-one.
On your point 1, regarding loss functions: I agree that a strictly utilitarian/consequentialist PoV would care about which side won, not about vote totals. I think there are three reasons to nevertheless build a loss function around vote totals.
1. Mathematically more well-behaved. For instance, the whole “MSE decomposition” idea I bring in later would be much much messier with a binary-outcome-based loss function.
2. I believe that in practice, if there’s a question where the target support would be, say, 70%, but the legislature supports it at 90%, you can probably use it to construct some other at-least-somewhat-reasonable question where the target support would be 40% but the legislature supports it at 60%. That is, in practice, errors in vote totals go hand-in-hand with errors in outcomes, even if this is not a logical necessity (at least, not without additional assumptions about convex lotteries and stuff).
3. Some of the votes/decisions of the legislature may be made in a non-majority-rules fashion. For instance, you could have some situations where each legislator gets to allocate a share of some resource. In such cases, the vote-total-based loss function is clearly correct even from a consequentialist standpoint. (This might be seen as a special case of 2, but it’s different enough to list separately.)
I think that saying 1 and 2 in the main article would be too much of a digression, but I will think further about whether there’s a way to include point 3.
Thanks for the close read and the thoughtful comments!
Open:
1. Loss function, future-oriented: interesting questions; I have thoughts on them; I left them out the first time through but may add them later.
2. gerrymandering; “infinite”; proposal I don’t fully grasp: Also interesting but I think beside the points I want to make here.
3. Dimensions.
“The choice of dimensions seems like a bigger deal than the number.” I’m implicitly assuming that they’re chosen by principal component analysis or something similar. Of course that’s not robust to scaling or other monotone transforms, but I think it’s close enough to being well-defined to handwave away for my purposes.
But if I’m wrong, and the variation in political opinions/interests that are politically salient in an ideal world is much higher, then the very “republican idea” of representative democracy is problematic.
“whether things interact with each other to greatly affect outcomes”: good point. I’ll see if I can incorporate it without being too wordy.
4. Weighted legislatures: yes, that’s a whole topic I could write an entire section on. For now, can’t afford to get that sidetracked, sorry.
“Variance seems like it might be a red herring, given a focus on outcomes/exemplariness.”
Um. It’s possible I’m not being clear what I mean by “variance”. I don’t mean variance of ideologies of legislators; I mean variance (meta-variance?) of distributions. That is to say, a 1-dimensional procedure for picking 2 legislators would have higher variance if it sometimes picked {5,5} and sometimes picked {4,6}, than if it reliably picked {0,10}.
I think there may something to your critique here aside from that possible misunderstanding, though. I have some thoughts but I’m not sure how I should or will deal with this issue. Probably, I should respond to that in a separate comment.
5.
“Weird methods:” Maybe I should explain how my existing proposal for rating voting methods would handle that? Because I have thought about it, and it is a tricky case. But I think I’ll save that for later; for now, I want to stick with simpler cases.
...
to be continued; probably in a separate comment or comments, for better notification.
(Currently complete, but subject to change with post—unless different versions are separate posts?)
Content:
Contents:
Content
Open
Addressed by document’s later contents
Style
(Numbering is within sections and only reflects order within text (appearance), but doesn’t cross categories.)
Open:
1.
I’m curious how this loss function differs from the results being the same, rather than the ratios. I’d guess that it would get smoother results, but the main issue would probably be interactions. (Systematic rather than random variance.)
The question of how to get a future oriented perspective seems an empirical one.
2.
Obligatory mention that gerrymandering might be detectable by measuring variance in outcomes (of elections).
But the election would take forever.
Unless people are organized into groups based around a group that literally negotiate over the tradeoffs, possibly reversing the ‘usual’ direction of voters → legislature. With the last step being the one that makes the Laws.
3.
The choice of dimensions seems like a bigger deal than the number.
And the question of whether things (like the factors captured by the dimensions, as well as ‘representability’) interact with each other to greatly affect outcomes (laws or whatever the means in question is that itself leads to outcomes).
4.
Why? Getting a more diverse set of perspectives seems doable via:
Electing one or more officials with different numbers of votes, but giving them power based on the number of votes they received. (Officials with less power may have less of an impact most of the time.* But if they’re able to bring new ideas to the table that work...)
*Ignoring the possibility of officials with powers based on circumstance, or within certain domains.
Variance seems like it might be a red herring, given a focus on outcomes/exemplariness.
5.
3a from the next section seems like it might be relevant.
Weird methods:
Representatives are chosen from Group A, but chosen by Group B voters. (There’s also changing power amounts as mentioned previously.)
6.
In some ways there seemed to be a similar circularity around the use for “utilitarianism” whcih seemed to mean ‘representativeness of democracy’ in context.
I look forward to seeing more in this section.
Addressed by document’s later contents:
1.
Based on the rest of this document, you mean a utility function*, or something else very different from utilitarianism.
This (later) part makes it more clear:
2.
Depends on the system—The utility is based on the actions of the legislature (and also it’s cost and thus size, especially if the people/voters have to pay for it).
(Later) Addressed here:
3.
a) Voters could also be selected to ‘create/represent’ conflict, and see which side wins. (If the remaining population that hasn’t voted isn’t big enough to overturn the current win/result, the voting stops, or the result is passed. (An error rate/margin could also be included.))
b) This could be reversed; the voters are selected in order to create a body in which
and where additional voters improve this probability.
c)
The question of cost is also a matter of global utility.
d)
If instead of voters voting, a body that deliberates on the question/s this can allow for more options being evaluated, and perhaps more “right” being found—though the bigger the body (and the search space), the longer this might take, and costs probably should be taken into account.
Later addressed here:
(And it may be different for “exemplary representatives”.)
Style:
on a footing
The multiple parenthesis are an interesting style choice.
The “ongoing” nature of this post is interesting and I like it. Having read it as it is, I think it worked really well, and some of the empty sections could fit together in a different post. Though since they don’t exist I don’t know how important the connections between them in one document are. (Maybe having this version as is might be useful.)
Key to strange punctuation I use: “((...))” are technical notes that you can safely skip if you don’t understand; the extra parens are to emphasize the skippability. ”))(...)((” are digressions that break the narrative flow, but are actually important; the inner normal parens are to mark digression and the doubled outer reverse parens are to mark importance.
Also I wrote TLD̦R instead of TL;DR (too long; didn’t read) because on my keyboard the semicolon is a dead key that combines with space or enter to be an ordinary semicolon but combines with letters to add accents. I think making TLD̦R one character shorter is in the spirit of TL;DR.
I’ve switched over to responding to your comments/suggestions one-by-one.
On your point 1, regarding loss functions: I agree that a strictly utilitarian/consequentialist PoV would care about which side won, not about vote totals. I think there are three reasons to nevertheless build a loss function around vote totals.
1. Mathematically more well-behaved. For instance, the whole “MSE decomposition” idea I bring in later would be much much messier with a binary-outcome-based loss function.
2. I believe that in practice, if there’s a question where the target support would be, say, 70%, but the legislature supports it at 90%, you can probably use it to construct some other at-least-somewhat-reasonable question where the target support would be 40% but the legislature supports it at 60%. That is, in practice, errors in vote totals go hand-in-hand with errors in outcomes, even if this is not a logical necessity (at least, not without additional assumptions about convex lotteries and stuff).
3. Some of the votes/decisions of the legislature may be made in a non-majority-rules fashion. For instance, you could have some situations where each legislator gets to allocate a share of some resource. In such cases, the vote-total-based loss function is clearly correct even from a consequentialist standpoint. (This might be seen as a special case of 2, but it’s different enough to list separately.)
I think that saying 1 and 2 in the main article would be too much of a digression, but I will think further about whether there’s a way to include point 3.
Thanks for the close read and the thoughtful comments!
Open:
1. Loss function, future-oriented: interesting questions; I have thoughts on them; I left them out the first time through but may add them later.
2. gerrymandering; “infinite”; proposal I don’t fully grasp: Also interesting but I think beside the points I want to make here.
3. Dimensions.
“The choice of dimensions seems like a bigger deal than the number.” I’m implicitly assuming that they’re chosen by principal component analysis or something similar. Of course that’s not robust to scaling or other monotone transforms, but I think it’s close enough to being well-defined to handwave away for my purposes.
“whether things interact with each other to greatly affect outcomes”: good point. I’ll see if I can incorporate it without being too wordy.
4. Weighted legislatures: yes, that’s a whole topic I could write an entire section on. For now, can’t afford to get that sidetracked, sorry.
“Variance seems like it might be a red herring, given a focus on outcomes/exemplariness.”
Um. It’s possible I’m not being clear what I mean by “variance”. I don’t mean variance of ideologies of legislators; I mean variance (meta-variance?) of distributions. That is to say, a 1-dimensional procedure for picking 2 legislators would have higher variance if it sometimes picked {5,5} and sometimes picked {4,6}, than if it reliably picked {0,10}.
I think there may something to your critique here aside from that possible misunderstanding, though. I have some thoughts but I’m not sure how I should or will deal with this issue. Probably, I should respond to that in a separate comment.
5.
“Weird methods:” Maybe I should explain how my existing proposal for rating voting methods would handle that? Because I have thought about it, and it is a tricky case. But I think I’ll save that for later; for now, I want to stick with simpler cases.
...
to be continued; probably in a separate comment or comments, for better notification.