(This essay concerns some of the constitutional changes proposed in A Sci-Fi Constitution.)
We Americans●● except Ben Franklin and Nebraskans in their eccentric wisdom celebrate our bicameral system. When working at its best, it protects individual rights by requiring broad national consensus before allowing our out-of-state neighbors from disabling the old rules that protect us, or from making new rules we have to follow. The measure of broad consensus is whether three different bodies (House, Senate, President) --- elected in three different manners on three different timescales according to three different spatial slicings-up of the country --- ALL agree that a proposed change helps more than harms.
To enhance this requirement of consensus, we might lean into the individual characters of the Congress's two Chambers. The ideal fairy tale goes like this: the House is a hot melting pot of diverse and zany passions, the stage for the People's grand polyphony; the Senate, a cool deliberator where even the less powerful States can claim a voice. I propose to strengthen bicameralism by making the fairy tale a bit more true.
The 17th Amendment was proposed and ratified in response to rampant corruption: State legislators in essence put Senate seats for sale. But the 17th Amendment's spirit, one of anti-corruption-via-popular-vote, can be preserved while also enhancing protections of local democracy: simply allow the State legislators to prepare the menu of candidates from which the People choose. Two desiderata: (A) even a lopsided legislature should produce a diverse menu, and (B) even if a majority of legislators are bribable and bribed, the menu should contain one or more "clean" candidates.
We kill two birds by letting minority groups of legislators nominate candidates. Let any group of, say, 1/5 of the State legislators●● The original Article I gives precedent for the U.S. Constitution breaking encapsulation to depend on the membership structure of individual State Legislatures. nominate one candidate, with no one belonging to multiple groups. Then the People by single transferable vote●● In this system, each voter ranks one or more candidates (1st, 2nd, etc). We'll do steps of elimination, so as useful shorthand let's say a candidate is at some step a voter's "favorite" when the voter ranks the candidate as best among un-eliminated candidates. The system is: SO LONG AS MULTIPLE CANDIDATES REMAIN, ELIMINATE THE CANDIDATE WHO IS THE FEWEST VOTERS' FAVORITE. (The remaining candidate wins.) Crucially, though candidates are eliminated, ballots are not: if my first choice got eliminated, then my ballot still matters in favoring my second choice over my third choice etc. select a winner.
Under a two party system, unless a legislature is 80-percent Blue or 80-percent Red, there will be at least one candidate from each major party. In fact, since SingleTransferableVote does not have major "spoiler" effects, we expect 4 candidates. Say a State's pro-Banana caucus, which originally would have nominated a certain pro-Banana candidate (who peels from the stem), is big enough that by splitting it could nominate two candidates. The half of those pro-Banana legislators who are sympathetic to a different pro-Banana candidate (who peels from the tip) would not jeopardize the pro-Banana cause if they split off to nominate that candidate; so we'd get two meaningfully different pro-Banana candidates. Legislators who want to avoid appearing complicit in narrowing voters' choices to just 2 --- a complaint apparently common among voters both Red and Blue --- and legislators whose ideas and emphases differ, even slightly, from the exact median preference of their party --- would be incentivized to increase the menu size. For this reason, there'd typically be 4 candidates.
Moreover, the SingleTransferableVote tends to reward moderation and civility. Mudslinging toward another candidate has the cost of worsening one's ranking on the ballots of those who like that candidate. Say the anti-Bananas are sufficiently more popular than the pro-Bananas so that it is a given that an anti-Banana will win; if the anti-Bananas are divided between one extreme and one moderate candidate, then the pro-Banana voters' rankings will tip the balance in favor of the moderate candidate. Result: a moderate anti-Banana candidate.
As for bribery: under the original Article I, a mere majority of (upper house) legislators could sell Senate seats; but in the typical multiple-groups scenario, unless 4/5ths of the legislators succumb to bribery, the people would have at least one "clean" candidate to choose. And since such bribery when it happens would be less effective, it would probably happen less to begin with.
The proposed change, in line with the 17th Amendment, has the People choose their Senator; moreover, the choice would, under our current two-party system, have the richness of primary elections in addition to general elections. The key difference is that it is subgroups of State legislators, rather than the local branches (and the primaries they have so much power over) of naion-wide Parties with national platforms, that select the menu. Thus, these candidates would tend to be more sympathetic to effecting the policies of the People --- whether these be Blue or Red policies --- via State government rather than National government.
The 1/5 threshold could have been any smallish fraction. I chose it for aesthetic unity. For, the smallest constant fraction that the old-and-actual Constitution mentions is 1/5: a minority of Senators or Representatives of that size may force the presentation (through their respective Chamber's journal) of information to the People. This lax threshold for information-flow to the People resonates with the proposed process by which State legislators recommend candidates to the People.
To amplify the House's direct and fiery character, one would want a voting system that FIXES GERRYMANDERING, and, more strongly, that is Concentration-Unswayed, i.e., that represents each minority no matter their geographic concentration. To illustrate, imagine two worlds: in World A, one third of all districts are entirely Star-Bellied, and the remaining districts are entirely Plain-Bellied. In World B, every single district is one-third Star-Bellied and two-thirds Plain-Bellied. The Star-Bellies should, of course, have one third of the House in World A. What I mean by Concentration-Unswayed is that the Star-Bellies should enjoy the same House representation in the two worlds. A Concentration-Unswayed voting system would, because it is impervious to gerrymandering and for other reasons, amplify the House's ideal character.
Yet, of the many Concentration-Unswayed voting systems, the better-known ones tend to rely on non-local representation. But Local representation is our American way. Your Representative's job●● unless you're in Puerto Rico or D.C. or a minor Territory; I'm sorry. is to represent you whether or not you voted for them, and likewise for all in your neighborhood. This softly rules out voting systems that enlarge our (already large) districts into multi-member districts or that, folding in our centuries-long resistance against pure factionalism, recognize Parties rather than People as the fundamental electable unit.●● One could maintain locality for these methods by radically enlarging or time-splitting the House or by complicated methods whereby local candidates affiliate with national parties that in turn rank their affiliates, so that, earning by global vote a budget of seats, their ranking and budget together determine which of their affiliates win --- hence the word "softly".
So, to get a Concentration-Unswayed, Local voting system seems to require some TURN-TAKING: I, Star-Bellied, agree with my two Plain-Bellied neighbors that I will get my candidate this election and they will get theirs in the next two. Making a table of who agrees with whom, we schedule which subgroups control which of the next several elections. Now, this is horribly complicated, especially as folks move within and between States; worse --- and this is a fundamental flaw if we seek democracy --- this remember-a-past-table method does not accomodate people who over time change their mind! We seek a system that is Memoryless.
Fortunately, there is a way out --- a very simple system that is simultaneously Concentration-Unswayed, Local, and Memoryless. In this system, the lifetime experience of a citizen (one engaged enough to vote) in their more than two dozen House elections, would be, if, say, they happen to be always in a minority of size one-third, that in close to one third of those elections their favored candidate wins. If half of the time they are in a minority of size-one-third minority and the other half in a size-two-thirds majority, then in close to half of their lifetime elections their favorite candidate will win. And so forth.
The system is this: select each election's winner with probability proportional to votes received, that is, randomly. With dice as our turn-taking mechanism, no memory is needed.
We, unlike 250 years ago, are a numerate nation. To the worry that "Whoever controls the dice controls the outcome" we may answer that the metaphorical die roll shall be the joint responsibility of the election's candidates, by any of the many methods of randomness-aggregation, relying on basic arithmetic, that are not just fair but in fact to-the-public-verifiably fair. Such systems have the properties that: (A) they generate randomness that will then by a deterministic process be used to threshold election counts, so that recounts can be performed with no problem; (B) unless the candidates unanimously conspire to cheat in a coordinated way, then the resulting die rolls are truly fair (example: if at least one candidate doesn't cheat, or if all Blue candidates cheat together and all Red candidates cheat together, but these two groups do not collaborate, then the resulting die rolls are truly fair); (C) ordinary members of the public, with pen and paper and spare weekend, or with a computer and a spare minute, can via basic arithmetic verify that an election outcome was fair, again assuming there is no unanimous conspiracy.
It would be understandable if one feels anxious about turn-taking. Something feels unfair about a 60-percent majority getting their way only 60-percent of the time, and in particular perhaps not getting their way this year! Here again, the facilitation via randomness of turn-taking establishes formal properties to assuage our worry. Key is that turns are uncorrelated between distinct districts. Switching viewpoint from that of single voters across all their years to that of single years across all their voters, we see by "Laws of Large Numbers" that the House in every year will have nearly proportional representation. How nearly? Say that about 50-percent of voters●● weighted, as usual, by voter engagement and by the ratio of each State's seats in the House to its population vote for the Star-Bellied cause. Then we expect with probability 95-percent (i.e., with exceptions only every forty years) less than 4.7 percentage-points of deviation from this quantity. For comparison, this once-in-forty-year deviation under the turn-taking system is a bit smaller than the current system's typical deviation of 6.3 percentage-points over the past 20 years.●● "6.3 percentage-points" is a root-mean-square, over 10 elections, of the difference between national House representation fractions and national voting fractions, and counting only the two major parties. Our computation of national voting fraction differs from a simple national sum-of-votes in two ways: (a) we normalize away voter engagement, so a district has the same weight whether its voters submitted 1000 or 100000 ballots, and (b) each district has the same weight; e.g. Delaware-at-large (population 1.0 million) and Wyoming-at-large (population 0.6 million) both have weight one. We count candidates who officially affiliate with Democrats or Republicans, and no others. When an election has multiple candidates of the same party, we sum their votes. We merge all parties with "Democrat" in their name (e.g. Minnesota's DFL), and analogously with "Republican" (no party counts as both). I used the MIT election lab's data.
We could eliminate very unpopular candidates by imposing a threshold before consideration for turn-taking. This may assuage fears of some Horrible Fascist Minority gaining a few seats among the House's many hundreds. Such fear is the typical anti-populist fear that is the bass line to the praise, which Blue voters give during Red eras and Red voters give during Blue eras, of indirect democracy with checks and balances. And indeed, not just the moat between "few seats" and "a majority of seats" but also our bicameral system (the House by itself cannot make law) give strong answer to the fear. Still, requiring a low threshold does little to erode the benefits listed and may calm the anxious mind. So we pick a fraction --- as in our discussion of the Senate, 1/5 has among various small fractions the benefit of aesthetic unity. Another way it phrase it is: if your candidate is so unpopular that it'd take longer on average than the time between censuses for their turn to come, then they are too unpopular to be considered. This is because 5 House elections occur between consecutive censuses.
Zooming out to our Bicameral theme: each seat of the House is a stage for expression, not wise consensus. We further this ideal via MemorylessTurnTaking, which fixes gerrymandering, and due to LawOfLargeNumbers faithfully reflects the electorate's makeup, and gives voice to minorities --- those we strongly agree with and those we strongly disagree with. Meanwhile, the Senate is the great moderator. We further this ideal by GroupNomination and SingleTransferableVote, the first installing a subtle moderating force toward State autonomy and the second a mechanism that helps moderate candidates --- those that unexcitingly unite supermajorities rather than intensely dazzle mere pluralities --- to win.
This pair of changes to how Representatives and Senators are elected has the pleasant property of political balance, for, as I gather, proportional House representation is considered a Blue cause, and State influence over the Senate a Red one. (Aside: to be honest, I don't understand why. Gerrymandering●● by which e.g. Maryland has hurt Red voters and North Carolina has hurt Blue voters, such effects by some metrics roughly canceling nationally hurts both Blue and Red voters and, more importantly, should offend the republican sensibilities of every American. As for the Senate as protector of local democratic self-government: #among the small States there are both many Blue and many Red States and, more importantly, the erosion of the power of States to self-regulate●● e.g. Blue voters may object that 2005's PLCAA enfeebles local democratic regulation of guns, or that judges confirmed by a modern Senate may, in interpreting the Comstock Act, prevent local democratic processes from ensuring abortion pill access; meanwhile, Red voters may object that 2010's ACA disables local democratic processes from determining how to balance the health of children against other costly projects has in this century been negatively felt and much protested by both the Red and the Blue.)
Summary:
ELECTION TO THE SENATE --- The State Legislature shall, in the May before the election, nominate a number of candidates, with any group of one fifth of its legislators duly sworn permitted to nominate one candidate; but no two groups shall overlap. And from these candidates, the people of the State shall by SingleTransferableVote elect their Senator. That is: each voter shall rank one or more candidates, and so long as multiple candidates remain, that candidate shall be eliminated who is, according to the voters' rankings of the candidates yet un-eliminated, the first choice of the fewest voters; the remaining candidate shall win.
ELECTION TO THE HOUSE --- The people of the State shall by MemorylessTurnTaking elect their Representatives. That is: the State Legislature having determined one district for each seat, each voter shall select one candidate; the district's winner shall be chosen, from among the plurality candidate and all candidates receiving one fifth of all votes, with probability proportional to votes received, and this randomness shall be independent of all other elections.
Here I'll explain how to craft a VerifiablyFair protocol by which several candidates in an election can jointly "roll a die" so as to pick a winner with probability proportional to number of votes received.
First, momentarily putting aside the issue of fairness, how can "die rolls" pick a winner? One way is to stack the ballots in alphabetical order --- first come all the ballots that mark "Alice", then all those that mark "Bob", and so forth. Next, randomly uniformly choose a number \(x\) between \(0.0\) and \(1.0\), and select the ballot that is a fraction \(x\) of the way from the start of the stack to the end: the candidate marked by that stack wins. Since each ballot is equally likely to be selected, the candidates have winning-chance proportional to the votes they receive, as desired.●● Since we imagined the ballots as stacked alphabetically, we don't have to actually physically stack them: it's easy to figure out what the outcome would be if we did stack them, based on \(x\) and on the election tallies; also, if a recount is called, we just use the same \(x\) together with the modified election tallies. Unless \(x\) originally landed very close to one of the liminal ballots between one candidate's part of the stack and another, or unless the recount drastically changes the tallies, the recount will not change the winner.
Now, how do use "die rolls" to choose \(x\)? Well, just as we can use two rolls of a \(10\)-sided die to get a number up to a hundred, we can use six rolls to uniformly randomly select one of the million numbers between \(0.0\) and \(1.0\) with six digit after the decimal place. As this resolution is more than enough for practical purposes, our task is reduced to VerifiablyFairly performing a joint roll of a \(10\)-sided die.
TODO
Say you've made an astonishing scientific discovery, but being a jealous and secretive person want to sit on it for a while before announcing it, perhaps to get a head-start building on it. Yet if you don't announce immediately, you worry that someone else will discovery the same, then by announcing their discovery will appear in the public eye to have scooped you. What should you do about this dilemma?
The 17th century solution of Hooke, Newton, and others was this: to announce a an anagram of a description of the discovery. The anagram was pretty hard to unscramble, so announcing it did not jeopardize the secret. But if a priority dispute arose, then the discoverer could reveal the original (unscrambled) description; though it was hard to unscramble the anagram, it was easy to check if any purported decoding was authentic. This is how these petty geniuses secured priority.
In modern times, we have better versions of the same scheme. Two problems●● A third problem is that the description of the discovery was sometimes quite vague, potentially amplifying problem (B); but this is neither here nor there. with anagrams of short latin sentences that Hooke et al used to describe their discoveries: (A) with large but plausible effort and luck somebody could unscramble the anagram, leaking the secret; (B) a "discoverer" could potentially contrive some super-flexible anagram●● probably with lots of vowels and common consonants to be "unscrambled" post hoc to any of a large range of descriptions. Basic arithmetic on large numbers helps us address both (A) and (B).
For example, there are fast algorithms for generating random prime numbers of a given number of digits. Generate two \(1000\)-digit prime numbers \(p\) and \(q\), then set \(n=p\cdot{}q\), their product. From the product \(n\) alone, it is very very hard to figure out \(p\) and \(q\) --- brute force, using a classical computer the size of the earth, would still require much much more time than the age of the universe. This will help us address (A). Yet by high school facts about factorization, there is only one answer: \(p\cdot{}q=q\cdot{}p=n\) and no other pair of integers-at-least-two multiplies to \(n\). This will help us address (B).
To put this to work, say that the "secret" we want to create an "anagram" for is some \(500\)-digit number \(s\). Appending to \(s\) a random \(100\) digits to get \(s^\prime\), and generating \(p\) and \(q\) (say for definiteness \(p\) is smaller), we announce both \(n=p\cdot{}q\) and the last \(600\) digits of \(p+s^\prime\). That's a mouthful, but the point is that (A) from the announced data we can't●● There are technically much better examples of the kind of "modern anagram" we are discussing --- examples we have even more faith are computationally intractable even by quantum computers --- but we'll stick with this example for simplicity. figure out \(s\); and (B) that from a further announcement (of \(n\) and a purported \(s\)) the public can verify whether the purported \(s\) coincides with the original \(s\).
ILLUSTRATION I --- To jointly roll a \(10\)-sided die, each candidate, prior to election, privately records a random digit (0 thru 9), sealing their digit in an envelope to be stored in the public trust. After election, the envelopes are unsealed and the joint outcome is defined as the last digit of the sum of the candidates' digits.
ANALYSIS OF ILLUSTRATION I --- The good case is where each candidate generates their private digit by actually random means, perhaps by rolling their own \(10\)-sided die. It's obvious that in this good case, the outcome is a uniformly random digit.
What's neat is that even with huge amounts of bad faith, the outcome is still a uniformly random digit. The two key properties are (A) that any one candidate's choice of digit can arbitrarily change the joint outcome and (B) that each candidate's choice , being private, affects neither the choices of other candidates or the ballots of the People. What guarantees (A) is that any digit can be gotten (as an answer's last digit) from any digit by adding the appropriate digit. What guarantees (B) is that the choices were made privately before the election, using the envelopes as a "commitment scheme".
For example, suppose the candidate Xavier is ganged up on by a conspiracy of all the other candidates. Since Xavier is late in the alphabet, the other candidates conspire to try to make the joint outcome small, close to 0 rather than 9. But if Xavier generates his digit by actually rolling a die, then no matter what the conspiracy does in response (which can't depend on the actual roll, by (B)) the joint outcome will be uniformly random (at root by (A)). Moreover, Xavier is by winning chances dis-incentivized from choosing an even somewhat-predictable digit; for, if Xavier indulged some non-random tendency (perhaps to choose his favorite number 7) then the conspiracy could exploit that tendency (in this case by choosing 3, so that the joint outcome is 0). That is, even if Xavier isn't intrinsically invested in good-faith behavior, so long as he does not cooperate with the conspiracy against him: the outcome will be uniformly random.●● Similar analyses establish the same outcome when, for instance, every candidate belongs to some conspiracy (perhaps there is a big Red conspiracy and a big Blue conspiracy), so long as these conspiracies are disconnected. The key tool in such analyses is the assumption that each candidate works rationally toward some goal (which does not need to be related to that candidate winning), and what justifies this assumption in practice is that in this "game of multiple added dice", rational behavior isn't trick or complicated to discern. Through more general analyses of the same kind, we find that: Unless the candidates unanimously conspire, the outcome will be a uniformly random digit.
... Now, Illustration I generates just one digit, but we can use the same idea to generate many random digits ...
ILLUSTRATION II --- To generate \(1000\) random digits, each candidate privately records a random \(1000\)-digit sequence in an envelope to be stored in the public trust.●● Practically, to save four hours of tedium, a trusted computer-saavy member of the campaign team does this by computer. After election, the envelopes are unsealed and the joint outcome is defined as the last \(1000\) digits of the sum of the candidates' sequences, regarded as numbers.
... Illustration II generates fair randomness but not verifiably fair randomness. The public can watch on TV how the envelopes were deposited, kept safe, and drawn out, but this is still a bit dissatisfying. How would a controversy be resolved in which a candidate claims their envelope's entries were tampered with? We can use the HASHING idea mentioned above to replace physical envelopes by a verifiably fair mechanism. ...
ILLUSTRATION III --- To generate \(1000\) random digits, each candidate privately records a random \(1000\)-digit sequence. Each candidate publicly announces a "hash" of their sequence, such that from the hash alone the sequence cannot be inferred and such that the public may, by comparing against the hash, check whether any purported sequence is the same as the actual sequence. After election, the candidates announce their private sequences, and the joint outcome is defined as the last \(1000\) digits of the sum of the candidates' sequences, regarded as numbers, counting only those sequences that, as checked against the hashes, were faithful.
ANALYSIS OF ILLUSTRATION III ---
●● One also must guarantee that each candidate's choice of whether or not to faithfully announce their sequence is not influenced by other candidates' announcements, a minor problem within the realm of problems already solved by current techniques to multiply supervise ballot-counting
Note: even if we want to use just a few digits of randomness, say 6 digits, it's important to have the hashed secret be many many more digits; for if the secret is only 6 digits, then by brute force (over a million possibilities, which is quite easy on a computer) the secret could be inferred from the hash.