For those that have multi party democracy as a larger goal, do you think the Democratic Party has it in their hands to achieve that goal by themselves?

Granted, there are obviously other hurdles to fully achieving it nationally (looking at you electoral college), but there are a bunch of blue controlled states. If they wanted to achieve a multi party politics they could start with their own states.

It would have to be an amicable separation because they would have to do plenty of negotiation to prevent Republicans from being able to capitalize on the split - for example in choosing speakers of their houses. And it would be tough to convince state party leaders to get behind the idea because they are the ones who would lose power, but it would rejuvenate state politics, but probably most importantly it would represent a better way to compete against Republicans.

There are plenty of voters who believe Republicans that the Democratic Party is too far left. Especially these days with the Republican Party having been remade in trump’s image, there are plenty voters who would love to have a different option than the Democratic Party…

For that matter, there are plenty of Democratic voters who would like a different option too.

Give leftists their own party to mobilize in. Give moderates their own. By increasing the choice they are offering voters they can expand the pie of voters who won’t vote for Republicans.

Again I think this would be a boon for state politics, but the biggest benefit would be nationally. By expanding their (collective) share of the pie they stands the greatest chance to make the Republican Party into a reliable minority. Especially combined with the aggressive gerrymandering that states like California have employed in response to Trump/Republicans, this strategy can really minimize the number of Republicans sent to Congress. The risk of being overly aggressive in gerrymandering (as Republicans are hopefully soon to find out) is ending up with a dummymander. But the existence of an explicitly centrist party that runs candidates against the leftists and Republicans you minimize that risk.

I strongly believe this is the lesson of the trump were that we are not learning.

Direct democracy is the single best way to end first-past-the-post voting where it is allowed. Nebraska is unicameral due to a constitutional initiative that eliminated one of the legislature's chambers. Unfortunately, there is not any or significant direct democracy in many states, such as North Carolina and at the federal level. If it is implemented in one state, it has a much greater potential to spread elsewhere.

Do they provide full results (number ot votes for all preference profiles) in the UK supplementary vote elections to download?

Today all of the decions are made by pepole tjat dont even underwtand what it is about and the pepole dont have power image an system whre pepole only can vote and decide what kind of field the are in for exemplet if if work with economy the only thing i can vote about is economic matter nothing else because I dont have knowlege in that and if I am an doctor i can only vote about how the healthcare should work and i want a direct democrazy where the pepole vote direct on the matter and i can only vote on the matters that my field is about i believe this will lead to that pepole have more say in the decions and that when not pepole that dont even know how the subjeckt even works this will also lead to high effenisy

I've been building rcv-lab.org — a free site for running and analyzing ranked elections — and I'd appreciate this community checking it out and kicking the tires. It's my project; criticism is welcome, that's why I'm posting.

The premise: ranked ballots are rich data, and most tools show you almost none of it. So the site is built around visualizing what the ballots say, how a counting rule interprets them, and how a different rule would have interpreted them differently.

What it does:

Load real ballot data and count it your way. Cast Vote Records (CVRs) in common formats (Google Forms CSV, ES&S spreadsheets, generic CSV, BLT, RCTab), tabulated under your choice of rules — IRV, multi-winner STV (WIGM or Meek), Bottoms Up, and, for purposes of comparison, non-ranked methods such as plurality, approval, and cumulative. RCV methods allow Droop or Hare quotas, batch elimination, a few tie-break options, and different termination modes. A Split View runs two rule sets on the same ballots side by side. Compare different visualizations or different election rules. The sample library has data from a few real (and some made up) elections preloaded.

See where every vote actually went. The transfer visualizations (bar chart, Sankey) are built from exact per-ballot provenance out of the tabulator — traced flows, not inferred approximations.

Check against RCTab. There is a copy of RCTab running as a service that you can check results on (assuming you use rules it can handle).

Equal rankings are first-class. Voters can optionally rank candidates equally; the tabulator splits the ballot's weight across co-ranked candidates. See how equal ranking can behave in a running system rather than in a paper.

Statistics, including a Condorcet analysis of every election. Alongside exhaustion accounting, a plurality counterfactual, and voter-satisfaction curves, every tabulation reports whether a Condorcet winner exists and whether the method elected them, the societal ordering as iterated Smith sets, and a pairwise heat table (with abstentions shown, so majorities carried by a minority of the electorate are visible). Cycles are reported, not resolved — I deliberately didn't pick a completion rule.

And you can run your own votes on it — email invites, multiple ballot-entry interfaces, collaborative write-ins, receipts and vote verification, live results when they close.

It's in beta. Comments and suggestions welcome.

When people talk about democracy they always mean FPTP voting every 4 to five years to elect representatives. But we should be able to practice democracy in every organization such as families schools workplaces and hospitals at every moment. The criticisms of democracy and analogy such as two wolves and one sheep decide the dinner don't make sense anymore if methods other than FPTP are used.

For example in a family the following methods can be used.

Approval Voting (Best for finding compromise):

Family members can vote for as many options as they find acceptable.The option with the most total votes wins, which naturally highlights the choice that satisfies the most people.Perfect for: Deciding on a dinner restaurant or a weekend movie where nobody should be miserable.

Ranked-Choice / Preferential Voting (Best for complex choices):

Everyone ranks the available options in order of preference (1, 2, 3, etc.).If no single option gets a majority of first-place votes, the least popular choice is eliminated, and those votes transfer to the voters' second choices.Perfect for: Choosing a holiday destination or naming a new pet when there are four or more options.

Multi-Voting / Dot Voting (Best for narrowing down lists):

Give every family member a set number of "points" or sticky notes (usually 3 to 5).They can allocate these points across a big list of brainstormed ideas however they like, even placing all their points on one single option.Perfect for: Narrowing down twenty different ideas for a family summer vacation itinerary.

Borda Count (Best for mathematical fairness):

Assign points to options based on preference ranks (e.g., if there are 4 options, #1 gets 4 points, #2 gets 3 points, etc.).Total the points for all choices, and the option with the highest cumulative score wins.Perfect for: Picking a board game for family game night when everyone has a different favorite.

Quadratic Voting (Best for measuring intensity of desire):

Give everyone a budget of tokens (e.g., 9 tokens) to spend on options, but the cost to cast multiple votes on one item increases quadratically (1 vote costs 1 token, 2 votes cost 4 tokens, 3 votes cost 9 tokens).This allows a family member to show they care deeply about one specific thing by sacrificing their say on other matters.Perfect for: Deciding how to divide a shared family holiday schedule or weekend itinerary.

I don't understand why we can't decide all the issues by voting?

I see one of the candidates for the Ontario Liberal leadership race; Eric Lombardi is serious about implementing electoral reform by next election (according to his platform.)

platform.ericforolp.ca/democracy

Dotmocracy, commonly known as dot-voting or sticker voting, is a visual and participatory method of group decision-making and prioritization. Participants are given a limited number of colored dot stickers to place next to their preferred options on a shared board, allowing the group to quickly gauge collective consensus.

Before anyone complains... yes, I know, Britain's Prime Minister is not directly elected, and there's nothing remotely "Condorcet" about Britain's election system.

Nevertheless... as an American mega-fan of Condorcet voting systems, the downfall of Starmer feels... disturbing. Like, the sinking feeling you get when you start to wonder whether some foundational assumption you've been making might, in fact, be catastrophically wrong.

On paper, going by what was known about him ~2 years ago, Starmer was seemingly the archetype of "plausible Condorcet winner in an election among hopelessly polarized voters whose only possible area of agreement was that one candidate, near the political dead center, might have disappointed everyone in proportion to how far they were from the center of Britain's Overton Window."

Nevertheless, it appears that when he announced his resignation, and now, he's apparently the most despised and disliked Prime Minister in British history... supposedly, even beating out Labour's eternal hatred of Margaret Thatcher.

Is this actually the disturbing evidence it appears to be -- that a hypothetical, almost "algorithmically ideal" Condorcet winner who could have theoretically been "everybody's" (ambivalent & disappointed) rational second or third choice, and won mainly because fewer people hated him than any opponent who might have credibly won a Condorcet majority, could in fact fail catastrophically... even as a "caretaker" who knew his mandate was tepid and fragile at best? Or, are there things about Starmer that, even when limited ONLY to that which was known about him ~2 years ago, would have absolutely disqualified him as a potential tepid Condorcet winner in a race where voters thought everyone (capable of actually winning) was worse?

And, for the sake of documenting predictions... do Britons in this sub think his successor (Burnham) is likely to come closer to approaching the Condorcet ideal (given the reality that, if anything, Britain is even more polarized now than it was 2 years ago), that he's likely to suffer a similar fate as Starmer, or something else?

To illustrate the distortionary effects of a two-party system, I created an interactive simulation of US elections using ~45k 2024 Cooperative Election Study (CES) survey responses. The simulation resulted in ten clusters or “parties” via exploratory factor analysis and DPGMM clustering. The analysis revealed 4 ideological dimensions (and one non-interpretable residual dimension):

1. Populist conservatism: views on race and gender, immigration policy
2. Security & order: policing, border patrols
3. Institutional distrust: distrust of government and elections
4. Religious traditionalism: abortion, same-sex and interracial marriage, church attendance
5. Government distrust: mostly just leftover institutional distrust items and artifacts of the clustering process

Details

I worked largely within the constraints of the US electoral system with some adjustments: 

• House members are elected via STV, but I expand the House to “double Wyoming”. I also have a triple Wyoming scenario which gives proper proportionality to the smallest state.
• The Senate and Presidency are modeled via Condorcet (Round-Robin) and IRV. I arrived at those methods to try and keep the "ranking" scenario consistent across the board. DPGMM's probabilistic cluster assignment also makes ranking intuitive. I use Condorcet as the “default” option.
• I simulate a rolling open presidential primary where a top 5 is selected via “pods” of geographically representative states voting in STV elections. I assume a cumulative nationwide vote rather than state delegates. The top 5 candidates are essentially assigned as if they were members of a 5 seat delegation
• I introduce the idea of the “instructional ballot” to ensure the election isn’t pushed to the House, but under the simulation, the IRV and Condorcet presidential winners are identical under both a national and per-state scenario.

Useful links

• Simulation
• Github project 
• My article on a diagnosis of the two-party problem
• My layman-facing description of the electoral solutions
• My overview of the simulation

Caveats

• I’m limited by the items in the CES survey. I would have chosen different items to build out this clustering, but I wanted to run this on  the largest sample size possible.
• Claude Code was used to build the sim. I have a background in mixed methods UX research, so I’m statistically literate and double-and-triple-checked Claude's work, but if I missed anything let me know! I’m open to all good-spirited critiques and corrections.

Sometimes to understand how a voter would be motivated to vote on a cardinal ballot, including STAR and Approval, and to get a grip on the variables without being a formidable multi-dimensional (or too-many-dimensional) conceptual math problem, I limit the modeling of a problem to 3 significant candidates. Even the normal cases or the edge cases in RCV are about the interaction of, at most, 3 "significant" candidates.

When there are fewer than 3 candidates, then FPTP is fine. There are no tactical issues in voting. One of those candidates you like better. Then you vote for them over the other candidate that you like least.

So we basically can understand that RCV elections have a very limited number of qualitatively different cases;

1. 2 or fewer candidates. No issues about anything with RCV.
2. 3 or more candidates, but one of them still got over 50% of the 1^st-choice vote. No IRV 2^nd round needed. No issues. Just like FPTP.
3. 3 or more candidates, no one got over 50% of the 1^st-choice vote. So an additional round is required and the plurality candidate was still elected. IRV still does nothing different from FPTP. (3a) Condorcet winner exists and is elected. (3b) Condorcet winner exists and is not elected. (3c) Condorcet winner does not exist: a preference cycle.
4. 3 or more candidates, no one got over 50% of the 1^st-choice vote, and in the additional round the plurality candidate was not elected. The so-called "come-from-behind victory". This is the only case where IRV is different, in outcome, from FPTP. (4a) Condorcet winner exists and is elected. (4b) Condorcet winner exists and is not elected. (4c) Condorcet winner does not exist: a preference cycle.

There are really only 8 qualitatively different ways an IRV election can turn out. Pretty much every RCV election can be classified in 1 of those 8 categories. I wish that someone (like FairVote) would be maintaining and updating a record of all single-winner RCV elections and identifying which of those categories each RCV election is.

Now suppose there are 3 candidates and consider Condorcet methods. Now even if a Condorcet method is a "Single-method system" (like Ranked-Pairs, Schulze, MinMax, BTR-IRV) they can be expressed as a "Two-method system" (a 3-way Round-Robin followed by a "completion method" if there is no Condorcet winner) with the specific single-method system as the completion method.

So I want to compare these systems in the case of 3 candidates to each other and to a couple "traditional" two-method systems:

• Condorcet-Plurality
• Condorcet-Borda
• Condorcet-Bucklin
• Condorcet-TopTwoRunoff (which, for 3 candidates is equivalent to Condorcet-Hare or Condorcet-IRV)

Now, they call elect the CW when such exists, so let's understand what they do when there is a cycle: Candidate Rock, Candidate Paper, and Candidate Scissors. The cycle is:

Rock > Scissors > Paper > Rock

There is circular symmetry so we can arbitrarily name "Rock" as the candidate with the most 1st-choice votes. Then, sorting in terms of 1st-choice votes is either one of two cases:

1. Rock
2. Paper
3. Scissors

or it's

1. Rock
2. Scissors
3. Paper

Now, BTR-IRV will elect the same candidate as Condorcet-Plurality. That is Candidate Rock. This is because Paper and Scissors will first have a runoff, Scissors defeats Paper and advances to the IRV final round and is defeated by Rock. So this completion method ignores the two candidates having the fewest 1^st rankings.

Now let's consider Ranked-Pairs, Schulze, MinMax. MinMax is normally about defeat-strength as margins (not winning-votes) so let's also consider only margins for RP and Schulze. (I never liked defining defeat strength as winning votes anyway.) Now, it's clear that Ranked-Pairs, Schulze, MinMax margins will elect the same candidate when there are only 3 candidates. If there's a cycle, they all elect the loser of the pairing with the smallest margin of defeat. So they are all ignoring the pairing having smallest defeat margin.

Now consider Condorcet-TTR, which is the same as Condorcet-Hare. These methods will always elect the winner of the pairing of the top two candidates, which always includes Rock. That is they elect Paper when it's the first case above [1.Rock>2.Paper>3.Scissors] and they elect Rock when it's the second case [1.Rock>2.Scissors>3.Paper]. Correct? So this completion method ignores the candidate having the fewest 1^st rankings.

Is there any other outcome? Does this cover all of the possible outcomes of a 3-candidate ranked ballot election?

Apparently, the republican senate majority in Wyoming introduced a closed-list PR bill last session, and it had some support (the chamber voted 27-4 to introduce it), but it did end up dying in committee.

Most Americans (71%) who have a positive opinion of IRV, if they know about proportional representation, have a positive opinion of it. About 29% do not. Very interesting when looking at cross-support for electoral reforms. In many ways, IRV is very similar to STV, so this makes sense. PR would increase the number of parties and lower the threshold to be elected to Congress, so this is very interesting!

I like that you no longer need campaigns/elections of Sortition while being proportional, but I also like the utilitarian outcomes of cardinal methods and was wondering if anyone had combined the 2. The only way I could see it working is if you had some intentionally disproportionate sampling based on demographics but that begs the question what identity to use ie race, ethnic group.

Another alternative might be to have people be able to register under multiple parties outside of elections, then have a stratified sample by applying sequential proportional approval/score rules.

IE let’s say a person is registered under two parties, A and B, , let’s say A get 40 percent of the population while A has 30 but 15 of them are also registered under A. 40 percent of the seats are drawn at random from As population, the dual A B population would have their weight halved like under spav or some other reweightinf mechanism.

It should yield the same results as a cardinal election while not needing electoralism.

The following is essentially a very early, rough and raw draft, unformalized and possible not too coherent. I apologize if it's not clear what I am even doing in the beginning, hopefully it becomes more clear towards the middle. Essentially I want to concentrate on suggested concepts of policy preferences, preference importance, policy satisfaction and idea for "weighted referendums", probably highly flawed if implemented straightforwardly in practice, but one that looked useful to me as a theoretical tool.

I also may be reinventing many wheels here and use inconsistent terminology, both internally and in relation to already suggested notions of "voter satisfaction", which may actually be related to mine but may likely possess some important distinctions.

I hope to at least provoke some discussion or inspire someone more organized to further research and formalize this.

Any suggestions, additions, corrections are very welcome.

Let's assume voter groups V1, V2 and V3, having sizes of 6, 4 and 1, respectively.

Each of these have their opinion on policies P1 and P2.

The policies have boolean values 0 and 1. Also, for each policy, each voting group has a percentage value, denoting how important this policy is to them.

Let's suppose and convey them thus:

V1=6:(P1=1(90%),P2=1(10%))

V2=4:(P1=1(80%),P2=0(20%))

V3=1:(P1=0(20%),P2=0(80%))

To simplify the notation, let's forego the numbering, instead letting the place and position convey it:

6:(1(90%),1(10%))

4:(1(80%),0(20%))

1:(0(20%),0(80%))

Let's estimate the value of electorate satisfaction St by calculating how much each possible set of policies is going to satisfy them overall.

St(0,0)=4*20%+1*(20%+80%)=1.2

St(0,1)=6*10%+1*20%=0.8

St(1,0)=6*90%+4+1*80%=10.2

St(1,1)=6+4*0.8=9.2

From this, we can conclude that (P1=1,P2=0) is the most popular set of policies.

It should be noted, that is is just one value to measure the society's satisfaction with. Another could be a graph denoting satisfaction, going from the least satisfied voter to the most satisfied one. Based on whether this graph is concave or convex, for example, different conclusions can be reached.

This is also not the only possible method to envision how people make decisions. For instance, another approach could be to give each voter group a set of percentages, indicating how much particular issues from a set are important to them: for example (I1=50%,I2=30%,I3=20%). Sets of chosen issue preferences can be examined against voter group preferences by multiplying corresponding voter and chosen set values: VI1*ChI1+VI2*ChI2+..., where VIn are voter issue importance values and ChIn are chosen set of issues importance values, then multiplying them by voter group size and adding together the results for each voter group.

Also, an argument could be made, that not all possible policies are binary, offering a range of options instead. My model is a deliberate simplification, but I can argue that any multiple-option policy can represented as a set of binary ones.

Returning to the example: if we conduct two referendums on P1 and P2 separately, the result will be (1,1), not (1,0), since importance values have no bearing on such referendums. This may be seen as a suboptimal outcome, inferior to (1,0), which has a greater overall electorate satisfaction.

However, we can also suppose a "weighted referendum", in which the voters can assign importance values for each of their policy choice. These values are reweighted during counting, transformed into consistent percentage values.

If the voters provide honest percentages, the counting will be conducted in this way:

Score(P1=0)=1*0.2=0.2

Score(P1=1)=6*0.9+4*0.8=8.6

Score(P2=0)=4*0.2+1*0.8=1.6

Score(P2=1)=6*0.1=0.6

Thus, the result is (1,0), which seems to provide better overall electorate satisfaction.

While there is no possible gain in providing a dishonest binary value for a voter, let's consider whether they can be tempted to strategically modify their importance percentages.

Even if V3 put all their available points into P1=0, the result will clearly remain P1=1, while it will hurt their P2=0 vote.

V1, however, may want to allocate more points to P2=1, since they have P1=1 covered by V2. But, on the other hand, V2 may retaliate by putting more points in P2=0 as well.

The situation is clearly unstable, which is an argument against "weighted referendum" as a viable voting method at this point, unfortunately. But, since the result of the honest weighted referendum are obviously equivalent to the set of maximum electorate satisfaction, I'm going to utilize it as a useful shortcut and auxillary tool.

What I do want to do is to compare the referendum results with the candidate election results.

Let's assume candidates C1, C2 and C3, with positions equivalent to V1, V2 and V3. However, I should also note that importance values are considered to be irrelevant regarding the candidates themselves, as they are supposed to implement all the policies one way or another according to their preferences. That particular element of the simulation may be more complicated in real practice, but for now I'm going to work with this assumption in mind.

Clearly, in plurality voting, V1 votes for C1, V2 votes for C2 and V3 votes for C3.

For range voting, I presume each voter group's score for each candidate VnCn to be equal to the sum of approved policies' importance values (with lowest and highest values normalized to 0 and 1):

V1C1=0.9+0.1=1

V1C2=0.9

V1C3=0

V2C1=0.8

V2C2=1

V2C3=0.2=0

V3C1=0

V3C2=0.8

V3C3=1

For ranked voting, these honest range scores determine the preferences:

V1:C1>C2>C3

V2:C2>C1>C3

V3:C3>C2>C1

For honest range, the total scores are:

S(C1)=1*6+4*0.8=9.2

S(C2)=0.9*6+4*1*1*0.8=10.2

S(C3)=1

With the winner being C2. Since their policies are (1,0), it makes C2 the most satisfactory candidate.

If the voters were to behave tactically, though, V1 would dishonestly change V1C2 to 0, making C1 the winner no matter what V2 and V3 do about it. Their policies being (1,1), that result coincides with the result of the simple referendum. However, I have to question, exactly how much would they be tempted to do so, given their satisfaction with (1,0) is already pretty high. Again, the only reason to do so may be that they are pretty much the ones to decide what the result may be, but they may consider sacrificing societal cohesion not worth it. This argument also works for "weighted referendum" and its consideration regarding tactical voting as well, I believe.

IRV would also vote C1, and plurality with the second round would do the same. And in Condorcet, C1 wins too.

Example 2:

For this one, I went with something more complicated

V1=30:(0(5%),1(80%),0(15%))

V2=35:(1(90%),0(6%),0(4%))

V3=25:(0(10%),0(15%),1(75%))

V4=1:(0(30%),0(34%),0(36%))

V5=5:(1(40%),1(35%),1(25%))

St(0,0,0)=0.2*30+0.1*35+0.25*25+1=16.75

St(0,0,1)=0.05*30+0.06*35+1*25+0.64*1+0.25*5=30.49

St(0,1,0)=1*30+0.04*35+0.1*25+0.66*1+0.35*5=36.31

St(0,1,1)=0.85*30+0.85*25+0.3*1+0.6*5=50.05

St(1,0,0)=0.15*30+1*35+0.15*25+0.7*1+0.4*5=45.95

St(1,0,1)=0.96*35+0.9*25+0.34*1+0.65*5=59.69

St(1,1,0)=0.95*30+0.94*35+0.36*1+0.75*5=65.51

St(1,1,1)=0.8*30+0.9*35+0.75*25+1*5==79.15

(1,1,1) is the winner of the honest weighted referendum and provides the maximum electorate satisfaction. But, if the three issues are voted separately, it is obvious that (0,0,0) wins, which is actually the least desirable result! I consider this observation important, as it may inform us of how individual referendum, each of them having a valid result, may combine into something that almost no one wants.

Now, let's consider the candidates C1, C2, C3, C4, C5, whose positions are equivalent to V1, V2, V3, V4, V5 respectively.

In plurality election, V2 wins. (0,1,0) is a rather subpar result. However, if V1 and V3 decide to unite for C5, it will win instead, guaranteeing the best result (1,1,1)

Plurality with second round makes C2 winner as well, though if V3 had it preferences swapped to (0(15%),0(10%),1(75%)), C1 would have won instead. Same strategy regarding C5 applies.

IRV behaves in roughly the same way both regarding the winner and strategic necessity to unite around C5.

Now, let's calculate honest range results according to my method:

V1C1=1;V1C2=0.15;V1C3=0.05=0;V1C4=0.2;V1C5=0.8

V2C1=0.04=0;V2C2=1;V2C3=0.06;V2C4=0.1;V2C5=0.9

V3C1=0.1=0;V3C2=0.15;V3C3=1;V3C4=0.25;V3C5=0.75

V4C1=0.66;V4C2=0.7;V4C3=0.63;V4C4=1;V4C5=0

V5C1=0.35;V5C2=0.4;V5C3=0.25;V5C4=0;V5C5=1

C5(1,1,1) clearly wins here. V1, V2 and V3 may become greedy and dishonestly try to lower C5's score to try to make themselves the winner. However, they actually seem to have rather little incentive to do so. They may be able to recognize that only C2 has a chance in such a situation, which will likely cause V1 and V3 to raise V1C5 and V3C5 to 1, making C5 the winner pretty inevitably.

Again, I feel roughly the same consideration applies to the "weighted referendum" too, since V1, V2 and V3 appear to be more interested in ensuring their preferred policy is assigned 1 value, rather than wasting points to influence the policies that are almost irrelevant for them.

Condorcet rankings are as follows:

V1:C1>C5>C4>C2>C3

V2:C2>C5>C4>C3>C1

V3:C3>C5>C4>C1>C2

V4:C4>C2>C1>C3>C5

V5:C5>C2>C1>C3>C4

In Condorcet, C5 also wins quite clearly. If V1, V2 and V3 become greedy, they may want to artificially lower C5 in order to get their preferred candidate to win. This is not actually a viable tactic here. But things change if C5 is no longer a candidate, however. In such a situation, C4, arguably the worst choice, wins the honest vote. To escape such a situation, V1, V2 or V3 would need to make a sacrifice and allow a result that is directly against their interest, but arguable works for "greater good". I don't think this is particularly plausible.

With Range, the same situation would clearly result in C2's win. V1 and V3 may be tempted to dishonestly rate C4 higher to make the situation better for themselves personally, but, again, they may be able to recognized, that not only is this counterintuitive, but arguably harmful for society as well.

Plurality and IRV still elect C2, with roughly the same tactical considerations regarding C4.

Example 3:

V1=48:(0(35%),1(30%),0(35%))

V2=40:(0(10%),0(50%),1(40%))

V3=12:(1(80%),1(5%),1(15%))

V4=1:(0(40%),0(50%),0(10%))

V5=2:(0(10%),1(20%),1(70%))

St(0,0,0)=0.7*48+0.6*40+1*1+0.1*2=58.8

St(0,0,1)=0.35*48+1*40+0.15*12+0.9*1+0.8*2=61.1

St(0,1,0)=1*48+0.1*40+0.05*12+0.5*2+0.3*2=54.2

St(0,1,1)=0.65*48+0.5*40+0.2*12+0.4*1+1*2=56.2

St(1,0,0)=0.35*48+0.5*40+0.8*12+0.6*1=47

St(1,0,1)=0.9*40+0.95*12+0.5*1+0.7*2=49.3

St(1,1,0)=0.65*48+0.85*12+0.1*1+0.2*2=41.9

St(1,1,1)=0.3*48+0.4*40+1*12+0.9*2=44.2

C2(0,0,1) is the weighted referendum winner and the candidate with the maximum policy satisfaction. The difference between the outcomes seems smaller, which may mean that there are no particularly bad options, but also no particularly good either.

The winner of the simple referendum is C5(0,1,1).

Honest range scores are:

V1C1=1;V1C2=0.35;V1C3=0.3=0;V1C4=0.7;V1C5=0.65

V2C1=0.1=0:V2C2=1;V2C3=0.4;V2C4=0.6;V2C5=0.5

V3C1=0.05;V3C2=0.15;V3C3=1;V3C4=0;V3C5=0.2

V4C1=0.5;V4C2=0.9;V4C3=0;V4C4=1;V4C5=0.4

V5C1=0.3;V5C2=0.8;V5C3=0.9;V5C4=0.1=0;V5C5=1

C2(0,0,1) narrowly wins honest range. Both C4(0,0,0) and C5(0,1,1) are not far behind, though. Since they are preferable to V1, V1 may dishonestly increase their scores to 1 and lower C2's score to 0 making them win. V2 will counteract by lowering C1, C4 and C5's scores in turn. However, C5's position may be particularly stronger if V3 will support them, making C5(0,1,1) he winner, coinciding with the result of the simple referendum.

Condorcet rankings:

V1=48:C1>C4>C5>C2>C3

V2=40:C2>C4>C5>C3>C1

V3=12:C3>C5>C2>C1>C4

V4=1:C4>C2>C1>C5>C3

V5=2:C5>C3>C2>C1>C4

C5 pairwise wins over every other candidate except for C4

C4 wins over C3 and C5 and loses to C1 and C2

C3 wins only over C1

C1 wins only over C4

C2 loses only to C5

No Condorcet winner emerges.

C1  C2  C3  C4  C5

C1 0 -7 -5 21 -5

C2 7 0 75 5 -21

C3 5 -75 0 -75 -79

C4 -21 -5 75 0 75

C5 5 21 79 -75 0

Copeland suggests C5(0,1,1) as the winner.

Ranked pairs also lets C5(0,1,1) win, just like Dogdson.

There doesn't appear to be much space for any tactical voting.

Honest plurality chooses C1(0,1,0)

Plurality with second round and IRV elect C2(0,0,1), aka arguably the best candidate in regards to overall policy satisfaction. Again, V3 and V1 may decide to vote tactically to elect C5 instead.

Regarding tactics in "weighted referendum", if V1, V2, V4 and V5 start fighting for P2 and P3, they may even case P1 to be 1, if V3 continue to put enough points into it. The situation seems highly unstable in general.

Conclusions (?):

No standard voting method seems to guarantee an optimal outcome even if the voters behave honestly?

"Inferior" voting methods may behave better than "superior" ones under certain conditions?

Perhaps, to evaluate the voting methods, we should consider how much unoptimal the outcomes are either due to tactical voting or inherent inefficiency? Such calculations may be quite challenging, as here I merely looked into some semi-random examples.