I kept needing a quick way to count ranked ballots for small groups (clubs, friends picking a restaurant, office votes), so I built a free calculator:

https://rankd.app/tools/ranked-choice-calculator

- Paste one ballot per line, like `Tacos > Sushi > Pizza`. Add `12:` in front for 12 identical ballots.

- It shows every round: who gets eliminated, where their votes go, and how many ballots run out of choices.

- There are Borda and Condorcet versions too, so you can paste the same ballots into each and compare winners.

- It runs in your browser. No sign-up, and nothing is saved.

The example on the page is a nice demo: Tacos leads round 1 but loses under instant runoff, and Borda and Condorcet pick yet another winner.

When two options tie for last, it eliminates the one that had fewer votes in the previous round. If they were tied every round, both go. I'd love to hear if you think a different tie-break rule is fairer.

Hi all,

Nanson's and Baldwin's methods are both very easy for determining who to eliminate in AV (below average borda score and lowest borda score respectively) but I was curious what would be the natural translation to when there's more than one seat available?

Baldwin's is simple in that it's always the lowest score, but with trying to adapt Nanson's to STV (proportional representation) do you still eliminate below the average? Below 2/3rds of the average for 2 seats, and so on?

The closest solution I've come up with is eliminating (total candidates - seats)/2 candidates... But I don't know if that ruins the intent behind taking the average borda score

Eliminating and recalculating the borda score of 30 candidates one by one would be very taxing on resources, so I'm trying to find a way to do it in chunks... But there doesn't seem to be any literature on it (from what I can find)

Anyone more knowledgeable about it able to give their thoughts?

The Canadian province of British Columbia used Instant Runoff Voting (IRV) or ranked ballots in 1952 and 1953. I am trying to recreate that magic within the limitations of our First Past the Post system.

Our province has three major parties—the New Democratic Party (NDP), the Conservative Party, and the Green Party. The NDP and the Greens are generally considered to be progressive, while the Conservative Party is generally considered conservative.

There are multiple strategic voting websites that hope to consolidate the progressive vote, but there is a unique dimension to BC politics that this doesn't capture. Since the NDP is a 'big tent' party that attracts both centre-right and centre-left voters, and because the environmental focus of the Green Party draws supporters who are otherwise conservative or progressive, voters of each party may have either of the two other parties as their second choice.

Given these dynamics, there is probably a voter out there for each of the six possible permutations:

• Conservative, Green, NDP
• Conservative, NDP, Green
• Green, Conservative, NDP
• Green, NDP, Conservative
• NDP, Conservative, Green
• NDP, Green, Conservative

I created an interactive map to capture this nuance and show the best vote for each permutation in each riding. https://rankedballot.ca/

Voters can create a ranked ballot depending on their own preferences, and see what choice best avoids their lowest-ranked party. Where their lowest-ranked party isn't competitive, it shows their first-ranked party. The data source is 338 Canada, a weighted aggregator of polling data.

The actual interface changes colour based on the first-ranked party.

It was first proposed almost 10 years ago and was last proposed last year's July. There needs to be more concerted awareness and promotions of this bill to grab Congress' attentions.

I'm not sure which voting systems are ideal but I'm certain FRA alone guarantees ending gerrymandering for good and make genuine multiparty governings a reality that many voting systems that are being experimented locally doesn't.

This is why focusing on passing the FRA should be a top priority above all else to finally end the fptp duopoly system regardless of localized voting systems that are being tested rn.

Earlier this week, I claimed that STAR voters are almost always better off rating people at the extremes, 5 or 0. Sass disagreed, arguing that a voter with no insight into how everyone else will vote will do better scoring their second choice a 4, and their second-to-last choice a 1. I believe his logic is that the score gives them a boost in the runoff round.

To resolve this difference in perspective, I asked AI to write a STAR simulation that compares the expected value of rating a second choice 4 versus 5 across many random elections. I then ran a bunch of trials and thought everyone might be interested in the results.

With 3 or 4 candidates, a voter with no information does better rating their second choice a 4. With 5 candidates it’s roughly a wash, and with 6 or more, a 5 is better.

There are two reasons the strategy changes as the roster grows. First, your first and second choices become less likely to meet in the runoff, so maintaining a distinction between them matters less. Second, the competition to get into the runoff is increased, so the extra point becomes more valuable.

Simulation Notes

• Each run simulates 250,000 elections.
• In each election, two scenarios are run where a test voter rates their second choice with 5 stars and the other with 4. The results are compared.
• Results are the test voter’s expected satisfaction, measured by their own ratings: their favorite winning is worth 5, their second choice 4, anyone else 0–3. Losing your favorite to your second choice costs 1 point; losing it to a candidate you rated 0 costs 5.
• Every other voter rates every candidate independently and uniformly from 0 to 5, and votes honestly.

Here’s an explanation of a version of STV+ known as the Ranked Ballot Remainder+ method. Please let me know your thoughts on this system!

Here’s how it works:

- 85% of MPs are elected from multi-member constituencies, each returning between 2 and 7 MPs.

- 15% of MPs are elected as regional top-up MPs.

- Each region would have approximately 19 MPs in total, including both constituency and regional representatives. This would result in a Droop quota of approximately 5% of the region-wide vote.

- Voters can choose to rank one of more parties in order of preference, and/or put an X beside the individual candidate they support from the party they ranked first. Independent candidates can run as a single-candidate list, and will have their own box on the ballot that voters can rank.

- In Canada, this system can be implemented by either merging 3-8 neighbouring ridings together, then removing one seat from each riding to serve as a regional top-up seat OR by merging neighbouring ridings to form 2-7 member ridings, while increasing the size of Parliament by only 15% to accommodate the additional regional top-up MPs.

To elect the riding MPs, here are the steps to follow:

1. Calculate the Droop Quota based on the number of votes in the multi-member district and the number of seats available.
2. Determine the seat quotas for each party by dividing the number of votes received by the Droop Quota.
3. Award each party a number of seats equal to the whole-number portion of its seat quota, leaving a fractional remainder. For example, a party with a seat quota of 2.40 would initially receive two seats, with a remainder of 0.40.
4. Assign seats to candidates within each party who have the most individual votes for the winning party/parties. This may result in some seats in the riding remaining unallocated.
5. If every seat in the constituency has been allocated, the process ends. Otherwise, proceed to the next step.
6. If there are remaining seats, the parties would be ordered based on their fractional remainders
7. Eliminate the party with the lowest fractional remainder one by one until a party reaches or exceeds the Droop quota, thus leading to a party winning that remaining seat.
8. The remaining seat is awarded to the unelected candidate with the most individual votes from the party that wins the seat under Step 7.
9. Repeat Steps 6–8 for each remaining seat, stopping once all constituency seats have been allocated. Before each new round, reweight the votes of the party that won the previous seat so that its adjusted seat quota equals its fractional remainder. For example, if the party’s seat quota was 1.20 after the previous round, its adjusted quota would become 0.20 for the next round.

Regional top-up seats use the same general allocation method as constituency seats, with the following modifications:

- The Droop Quota is based on the number of votes in the entire region and based on the overall number of seats in the entire region (riding + regional top-up)

- Regional top-up seats are allocated to unelected candidates based on their party’s performance in each constituency. For each party, the candidate with the most individual votes in a constituency is eligible for a top-up seat, with only one candidate eligible per constituency. Candidates are prioritized according to the percentage of the local vote their party received, with the party’s strongest-performing constituencies prioritized first.

- If a party or independent candidate wins more constituency seats than their regional seat quota entitles them to, recalculate the regional top-up allocation. Remove all of the votes associated with the overrepresented party or independent candidate and reduce the Droop quota calculation to account for the constituency seats already won by that party or independent candidate

What happens if a party has ran too few candidates in their riding or region:

A party may receive enough votes to qualify for more seats than the number of candidates it has nominated in a constituency or region. The following rules apply.

- If a party’s seat quota exceeds the number of candidates it has nominated, its fractional remainder is calculated by subtracting the number of candidates it ran from its seat quota. For example, if a party has a seat quota of 1.73 but nominated only one candidate, its remainder would be 0.73 (1.73 − 1.00 = 0.73).

- If one or more parties have a projected seat entitlement greater than the number of candidates they nominated, their remainders are transferred first. These parties become ineligible to receive any of the remaining seats in that constituency or region, as they do not have enough candidates to fill them.

How bad is it, really?

What are the key points of Meloni’s reform?

• Abolition of single-seat constituencies (“ending FPTP”)
• A jackpot model for both houses: a proportional system based on current districts plus a winner’s bonus (jackpot)
• In the Chamber of Deputies, the coalition coalition with the most votes receives a bonus ensuring it holds 56% of the seats, capped at 70 bonus seats (out of a total maximum of 220 seat), provided it secures at least 42% of the vote (and also that it fulfils the same criteria in the Senate). The remaining seats are distributed via proportional representation (nationwide), while the 8 seats for overseas voters are handled separately (which is why I didn’t write 55% as the jackpot figure). In the Senate, the bonus and seat cap (57.5%, or 113 seats, excluding the 4 overseas seats) also apply at the national level, but seat allocation is regionally proportional. Consequently, the Senate’s system introduces a slightly higher degree of distortion.
• The electoral threshold remains at 3% (10% for coalitions)
• Special rules apply to Valle d’Aosta and Trentino-Alto Adige/Südtirol (votes and seats from these regions count towards the majority bonus and the seat cap, but not towards the proportional allocation).
• The number of “overseas” constituencies is also being reduced, though the number of seats remains unchanged. In the Chamber of Deputies, the number of districts is dropping from four to two, and in the Senate, from four to one. Consequently, de facto single-seat constituencies are being eliminated here as well.

All in all, the system does not strike me as being as bad as it could have been, or as bad as I had anticipated. Subjectively, I would rank the systems seen so far as follows (bearing in mind that potential translation errors or a lack of high-quality secondary sources might have led me to misinterpret aspects of the text passed by the Senate):

1. Pre-1993 system
2. Gutted ‘Porcellum’ (i.e., ‘Consultellum’, 2014–2015)
3. ‘Melonellum’ / ‘Stabilicum’
4. Partially struck-down ‘Italicum’ (2017)
5. ‘Italicum’ (2015–2017)
6. ‘Porcellum’ (2005–2014)
7. ‘Rosatellum’ (2017–2026)
8. ‘Mattarellum’ (1993–2005)

To explain a bit: proportionality carries significant weight for me, and I also favour open-list systems that offer the greatest possible freedom of choice. However, I consider it equally important that, if a system deviates from these principles to achieve a specific objective, it does so using a mechanism that is coherent, logically aligned with that objective, and reasonably effective. Furthermore, it is crucial to minimise the risk of misleading voters, to ensure that voting can be as sincere as possible, and to limit the scope for organised manipulation of the system. In light of this, I currently view the ‘Melonellum’ as the best Italian electoral system adopted by parliament (rather than one created by the Constitutional Court) in the last 30 years. I make this assessment by examining the system—unlike its architects—from behind a "veil of ignorance"; that is, I do not consider whom it might happen to favour.

https://electoralsystems.substack.com/p/habemus-melonellum-the-new-electoral

Most poll apps that I found seemed to either use FPTP, cost money, or leave a lot to be desired feature-wise. I made this site for my own personal use but figured that people on this sub may find it useful as well.

It appears that when faced with the options, people do not tend to pick the winners of IRV or Condorcet. Borda/antiplurality winners are more preferred. This seems to have the unfortunate implication that the methods people actually find intuitive/lead to desirable outcomes are the ones that are the most susceptible to strategy, while the better/more resilient methods like Condorcet (or the more common IRV) lead to outcomes that are somehow distasteful, or at least are founded on normative principles that many appear not to find desirable.

> "The rules that best-describe our subjects’ ordinal aggregation preferences are easily manipulable. When designing markets, establishing voting rules, or selecting aggregation procedures for other practical settings, the pursuit of non-manipulable (or difficult-to-manipulate) procedures may therefore render outcomes less normatively appealing to most of the affected parties."

The authors mention Approval in passing, but the desire for compromise makes me wonder if Approval is actually significantly more intuitive to the public than the Condorcet criterion (despite the apparent disproportionate representation in the reform space of those who find the Condorcet criterion so essential as to dismiss all other alternatives), but that is speculation.

As intuitive as the promises and normative foundations of Condorcet/IRV are, when the rubber meets the road, participants seem uninterested in the outcomes strict adherence to them would produce.

I've written a piece for The Loop (ECPR) discussing the case for establishing a National Commission on Electoral Reform before any major changes to the UK's voting system.

The article argues that:

• First Past the Post is facing growing criticism over disproportional outcomes.

• Concerns about the relationship between electoral systems and populist parties deserve serious consideration.

• Constitutional change should be based on broad democratic legitimacy rather than rushed legislation.

I'm interested in hearing arguments from supporters of both FPTP and PR.

Article: Why we need a National Commission on UK electoral reform 

Are the major claims made by this organization actually true?

Claim 1: * "In a majority winner system, candidates have to gain the support of more than half of the voters to win." ... "Using ranked choice voting in general elections requires candidates to win with majority support (more than 50%)."

Special election for Congress August 2022: 1. 188,582 voters voted in this election for a candidate (not a blank ballot). 2. The candidate who won received (counting votes the IRV way) 91,266 votes. 3. 91266/188582 = 0.483959 or 48.4%. 48.4% is not "more than 50%". 4. 91266 voters supported the winner (although 15467 were really supporting Begich). 188582-91266 = 97316 voters did not in any manner support the winner. More voters came to the polls and voted and voted for a loser than the number of voters who voted for the winner. 6050 more voters voted for a loser than voted for the winner. Would we allow a winner in an FPTP election to get away claiming they got "majority support" when more voters voted against that candidate than voted for them? 5. Compare apples to apples.

Claim 2: * "Ranked choice voting ... eliminates the spoiler effect"

1. Sarah Palin was the spoiler in that election. Had Sarah Palin not run and Alaskan voters come to the polls and voted exactly the same way with the remaining two candidate, then Nick Begich would have defeated Mary Peltola by a margin of 8408 votes.
2. The complete quote is "Ranked choice voting allows voters to rank candidates in the general election in order of preference. This gives Alaskans more choices, eliminates the spoiler effect..." Giving Alaskans the choice to choose Nick Begich over either Mary Peltola or Sarah Palin is irrelevant if that expressed choice is ignored.

Mary Peltola in August 2022, unfortunately shares a distinction with George W. Bush in 2000 and with Donald Trump in 2016. All three candidates were elected to office when the public record indicates that more voters marked their ballots preferring a different specific candidate for that office.

In August 2022, more Alaskans, 87859 to 79451 (an 8408 voter margin), preferred Nick Begich to Mary Peltola and marked their ballots saying so. But Mary Peltola was sent to Washington to represent the Alaskan people in Congress.

In November 2024, again, more Alaskan voters marked their ballots that Begich is preferred to Peltola by nearly the same margin, 7876 (164861 to 156985). But this time Nick Begich is sent to Washington.

Both times about 8000 more Alaskans said they would prefer Begich to Peltola. And, both times, marked their ballots saying so. Both times Instant-Runoff Voting was used.

What was different?

Sarah Palin was in the race in 2022 and not in the race in 2024. And the outcomes were different winners.

Here are the reasons we want Ranked-Choice Voting. The purpose of RCV is, in single-winner elections having 3 or more candidates: 1. ... that the candidate with majority support is elected. Plurality isn't good enough. We don't want a 40% candidate elected when the other 60% of voters would have preferred a different specific candidate over the 40% plurality candidate. But we cannot find out who that different specific candidate is without using the ranked ballot. We RCV advocates all agree on that. 2. Then whenever a plurality candidate is elected and voters believe that a different specific candidate would have beaten the plurality candidate in a head-to-head race, then the 3^rd candidate (neither the plurality candidate nor the one people think would have won head-to-head) is viewed as the spoiler, a loser whose presence in the race materially changes who the winner is. We want to prevent that from happening. All RCV advocates agree on that. 3. Then voters voting for the spoiler suffer voter regret and in future elections are more likely to vote tactically (compromise) and vote for the major party candidate that they dislike the least, but they think is best situated to beat the other major party candidate that they dislike the most and fear will get elected. RCV is meant to free up those voters so that they can vote for the candidate they really like without fear of helping elect the candidate they loathe. All RCV advocates agree with that. 4. The way RCV is supposed to help those voters is that if their favorite candidate is defeated, then their second-choice vote is counted. So voters feel free to vote their hopes rather than voting their fears. Then 3^rd-party and independent candidates get a more level playing field with the major-party candidates and diversity of choice in candidates is promoted. It's to help unlock us from a 2-party system where 3^rd-party and independent candidates are disadvantaged.

RCV failed, in Alaska in August 2022, to do precisely what it was adopted to do (essentially to prevent a spoiled election due to vote splitting, as a result punishing Palin voters for marking their favorite as #1 which caused the election of Peltola). The fault is not in the ranked ballots (in fact, it's only because of the ranked ballots that we know that Begich was more preferred by more voters than either Palin or Peltola). The fault is in the manner (IRV) that the vote is tallied.

This same failure occurred in 2009 in Burlington Vermont. Got published here.

This op-ed in Washington Post from November 2022 also spells this out. Written by two internationally-recognized election law and voting systems profs. One has a Nobel for his work.

Whoever tells us that RCV (using Instant-Runoff Voting tabulation) will solve the split-vote problem ("Can't split the vote in Alaska because we have RCV.") is lying. And Alaska in August 2022 is the proof.

To clarify, I’m sure I can use spreadsheets and the voters themselves could “easily” do xyz.

I know the idea is that “well, for very important decisions we want x” and “for simple stuff we want x.” For the more complex stuff, you probably want the chance of voter fraud, and a system like this. They cancel each other out. For simple stuff, approval is really good.

What about for stuff inbetween though? Student Government elections, maybe even your local club presidency election, but my main interest how this could be applicable to research. We love our 9 point scales and binary systems, but what if these things are contributing to Examiner’s Bias. As a very intersectional person, I just want to use this for my future intersectional research. Food for though.

Especially in the US, where you're starting with a very strong two party legacy system. I.e. let's say you use 'normal' approval voting for a swing state, that's 51% Red and 49% Blue in your election. Assuming an equal number of voters from both parties only approve of candidates from their own party, you've essentially recreated bloc voting- you would turn 51% approval into both slots in the second round being from the same party. Bloc voting is capital b Bad- one of the few ways to make FPTP worse. Let's not do that.

If you use sequential proportional AV, by my napkin math you could ensure that the second round contains a representative from each party until about maybe 65% of the state's voters vote for the same party? I.e. A party needs about two-thirds of the electorate to monopolize both runoff positions. But- you could also tweak the rules of sequential proportional AV- assign the second vote a value of .45, or .425, or .4, or .375, etc.

If you use full proportional AV, I believe the same general rule holds? A party needs two-thirds of the electorate to own both second round seats? Do you guys think one system is better?

I think you can absolutely debate whether a Republican deserves a second round slot, if their party only got say 37% of the vote statewide. I don't have the answer either way- I'm open to hearing peoples' thoughts. Let's be realistic and acknowledge that we're starting from a two party system though, not pretend that America has political parties that don't actually exist yet