What weaknesses could someone exploit to manipulate this "Approval plus RCV" electoral system?

Question

Question

I know that there must be ways that this system can be manipulated, but I'm having trouble figuring out what they are. I imagine that, since I created this system, I'm simply too close to it to see where exactly it would go wrong. For the story I want to write, someone (who, exactly, is yet to be determined) will be trying to manipulate the system to their advantage, so I need to figure out where the weak points are.

But at the same time, if the weak points are too obviously weak, I think it would be beyond the reader's reasonable suspension of disbelief for me not to fix them to a certain extent. I need a system that's reasonably sturdy for this person (or group of people) to still make a serious attempt to manipulate it and I am hoping that, with minimal tweaking, this is the system that will get me there.

To re-phrase the same question: What attack vectors exist in this system that a "bad actor" could exploit to their own advantage?

One potential angle, which I was recently reminded of (thank you @Mark), that I'd like a more knowledgeable person than myself to expand upon is Arrow's Impossibility Theorem. While this system certainly wouldn't have a dictator, I'm not yet very confident in my ability to thoroughly judge the other three criteria.

Everything beyond this point is a description of the system as I currently imagine it. I have many ideas to expand upon the government structure and the nature of checks and balances in this world, but I am trying to keep this down to only the relevant information. Feel free to request any such omitted details that you think may be relevant and I will edit to include them, if necessary. Assuming that I can appropriately tweak this system, I plan to ask further questions regarding the other aspects of this government I've envisioned.

Election Schedule

Elections are regularly scheduled, not called at the whim of the current party or parties in power.

Ballot

At its core, the voting system in this fictional world is a combination of approval voting and ranked-choice voting. Voters can approve of as many candidates for an elected office as they wish and must rank, at the very least, all of their approved candidates (although they can rank any/all of their unapproved candidates, as well).

I currently imagine that the ranking of unapproved candidates would, to voters, seem like a vote of "tolerance" rather than "approval." In other words, this is where voters would be ranking the "lesser evils," in their opinion, among the candidates. Ballots on which voters rank some candidates but approve of none will still be accepted, as will blank ballots with no rankings or approvals. Each of these "statement ballots" will have meaningful effects upon the election of candidates to office and, to a certain extent, their powers while in office.

Step 1 (Approval)

Once ballots have been submitted and the election workers are beginning to process the votes, the first piece of data they will be concerned with is each candidate's approval rating. Depending upon the number of seats per constituency an office elects, an approval threshold will be set (outlined below) beyond which a seated candidate will be said to have a "mandate." Whether or not a candidate has a mandate is based solely upon original approval and not subject to subsequent adjustments through the "satisfaction" process outlined in Step 3.

So long as at least one candidate is beyond the approval threshold, only those candidates beyond the approval threshold will be considered for being seated at all. If only one candidate is beyond the threshold, then they immediately win the seat in question without considering voter rankings at all. If there are still seats left to be filled, but no remaining candidates are beyond the threshold, then all candidates will move on to the next step, where they will be judged based on voter preferences.

Importantly, if a candidate is seated without a mandate, they will have certain limits placed on their powers in office and may even face electoral consequences such as a shorter term length or easier recall.

Single-Seat: For any office that elects only one member per constituency, which I will mostly limit to the Executive branch, candidates receive a mandate when they surpass 50% approval.

Referenda: For all intents and purposes, votes on various competing referenda would follow the same process as Single-Seat offices, merely replacing candidates with the various legislation under consideration. They would need to surpass 50% approval to receive a mandate and, if no legislation receives such a mandate, may be subject to certain limits as prescribed by the legislature.

Multi-Seat: For any office that elects multiple members per constituency, an approval threshold will be set equal to the reciprocal of the number of seated officials. For instance, if a congressional district seats five Congresspeople, then the threshold will be $\frac{1}{5}$, or 20% of all ballots. As a rule, all Multi-Seat offices are of equal size to their counterparts nationwide (e.g. congressional districts won't vary in the number of Congresspeople they elect). Also, any drawing of electoral districts would be done without regard to internal borders (so a national congressional district could cross state lines, a state district could cross county lines, etc.).

Step 2 (Preference)

For each candidate under consideration, election officials will determine how many ballots exist on which the candidate is either unranked or the lowest-ranked of the remaining candidates. For instance, if five candidates are still under consideration, officials will count up the ballots on which each candidate is not ranked among the top-four of the remaining candidates. The candidate with the highest total of such ballots is eliminated from consideration for the current seat in question and the process is repeated for each successive round until a winner is chosen for that seat.

Of course, should any candidate, on more than 50% of ballots, be the top choice among candidates still under consideration, then that candidate will automatically win the seat. Since it would be impossible for any other candidate to surpass them, no matter how many other candidates remain in opposition, there would be no point in continuing the elimination process for that seat.

Single-Seat/Referenda: I don't believe that any further steps are necessary when choosing a single winner.

Multi-Seat: After each elimination, election officials will determine if any remaining candidates are the relative top preference on more ballots than the approval threshold and, if so, make note of it. This is the percentage of ballots on which they are ranked higher than any other remaining candidate, as opposed to the absolute top preference, where they are the top-ranked preference among ALL candidates (including those that have been eliminated). Both of these numbers will be important for Step 3, to which Multi-Seat elections will now proceed after selecting any seat other than the final one for their constituencies.

Part 3 (Satisfaction)

After each seat has declared a winner for a Multi-Seat office, but before moving onto the next seat, changes must be made to the weighting of ballots. In order to ensure that Multi-Seat offices are as representative of the preferences of their constituency as possible, a weight of "satisfied" ballots equal to the approval threshold for that office must be removed. For instance, if a congressional district seats five members, then the total weight of ballots must be reduced to 80% of the original ballots after filling the first seat, 60% after the second, and so on.

In order to determine which ballots are satisfied, election officials will refer first to the absolute preference numbers for the seated candidate. If a candidate was the absolute preference for a larger percentage of voters than their required threshold, then the weight of those ballots will be discounted by the exact value of the approval threshold. For instance, if the just-seated candidate in a five-seat congressional district had 25% absolute preference, then those ballots will be reduced to $\frac{1}{5}$ of their previous weight (25% absolute preference - 20% threshold), or a collective 5% of the original ballots moving forward.

If the just-seated candidate had an absolute preference lower than the approval threshold, then those ballots will be considered "fully satisfied," zeroing them out and leaving them without even a slight influence over any remaining seats. Officials must then account for whatever portion of the approval threshold remains unsatisfied by referring back to the point at which their relative preference numbers pushed them over-the-top. Those ballots will then be discounted accordingly, in the same manner as described earlier for absolute preference ballots that extended beyond the threshold. For instance, if 3% of the threshold was still unaccounted for and, at the point of surpassing the threshold, an additional 5% of ballots pushed the candidate over-the-top, then those ballots would hold $\frac{2}{5}$ of their previous weight going forward.

After these adjustments have been made, election officials will circle back to Step 1 for deciding the next seat, which will make all inclusion/exclusion decisions based upon the new reference frame, without regard to the seated candidate(s) or the "satisfied" weight of the original ballots. They will continue to circle through all three steps until all seats have been filled.

For those uninitiated to RCV systems: To see why these adjustments are important going forward, consider a situation where two candidates who appeal to a very similar swath of voters within a 5-Seat district. Both candidates receive a mandate from the unadjusted original ballots, but only one can win the first seat in the district. Candidate A wins the seat. Candidate B had barely qualified for a mandate, with only 21% absolute approval, and Candidate A had been approved on 100% of those ballots. After satisfaction, Candidate B's approval gets knocked down to 1% of the original ballots within the new reference frame. Now, Candidate B won't be under consideration for another seat until no remaining candidates are above 20% relative approval. And even then, Candidate B will be largely at the mercy of voters who don't approve of them but ranked them as more tolerable than other candidates.

Answer 1

You're using a mixed set of approval votes, STV and AV. I was expecting to find some PR in there as well, but it was not to be (unless I've missed it). I expect your multi-seat will go on party list rather than individual candidate.

Approval voting

I have seen combined Approval/AV voting used in the wild. Candidates had to pass approval then win sufficient votes to be elected. To an extent, it works, it makes voting considerably more complex and doesn't really gain you anything over a plain AV/STV system. Where it really comes into its own is when combined with FPTP. It's entirely possible for no candidate to pass approval. If there's particular bad feeling between the main parties it'll probably happen in almost every constituency.

Problem: What do you do when no candidate passes approval?

STV/AV voting

(Also known as instant runoff voting)

I refer to these together since from the voters' point of view they look very similar, they rank as many candidates as they choose in order of preference on the ballot paper.

The key difference that STV and AV give in elections is the breaking of the two party system that FPTP favours. It's used fairly widely in practice and ensures that the winning candidate(s) have an acceptable proportion of the vote, either a threshold in cases of multiseat or a simple 50% when single seat.

The outcome of this will be to increase the number of parties represented in the government and increase the likelihood that the government will have to be a coalition rather than a single party. This effect is relatively normal in European governments.

Problem: Coalitions can have trouble passing legislation

What can your bad actor leverage

Not a lot unless in a position of power. The real position of power here is to be the "kingmaker" in a coalition, to be the leader of a party or faction that's required by the largest party to be able to form a government without having to turn to the primary opposition.

In the real world

Approval voting is not often used. Otherwise you're not asking much out of the ordinary.

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Why party list

Consider a healthy democracy. There are 3-5 major parties, another 12 minor parties in a constituency with 5 seats. Each candidate is listed name, address, party.

The major parties will list at least 1 candidate per seat. The minor parties will try to do the same but might not be able to, let's give them 2-3. You're now looking at a list of at least 50 candidates to approve and then rank for election. Not even the most enthusiastic voter is going to get more than halfway down that list, they'll try to find all the candidates for their preferred party and then stop.

Problem: Candidates further down a long list are less likely to be elected.

Since they might as well be voting for the party, let them vote for the party. You'll need a counting system that can cope with that, but there are more ways of counting STV than you can include in a short PhD dissertation.

Excessive democracy does not improve the health of your democracy, it just gives you a way to obfuscate what's really going on.

Answer 2

Systems like this are perfect only in paper. At the end of the day, the more human factor involved in the election, the more open it is to fraud.

For example, as someone who is counting votes, I might simply count wrong, erring on purpose to make my candidate the most approved one. Sure, in order to avoid such a thing there are measures such as validation by a third party, UN observers etc... But unless your country population is less than a handful, there will always be breaches.

Electronic ballots are no help in such cases. They are worse than human factor. They simplify the frauding effort. Rather than tricking, bribing or threatening who knows how many people, you only have to hack a machine.

There are other methods to exploit the system as well. Some author, I believe Terry Pratchett, once wrote about a people that employed democracy through open civil war. The principle is really simple: only the living get to vote, so if you kill enough voters that think different from you, you make sure that your side will get the most votes when the election comes.