[EM] OllPoll - score-based majoritarian party-list proportional representation method
Oskar Stolc
ollpoll26 at ostolc.org
Wed Jul 1 06:35:17 PDT 2026
Hi again,
I stumbled upon bettervoting.org, an online Reweighted Range Voting
calculator website. It showcases a sample election with 3 parties
(purple, orange, yellow), 5 candidates in each party, and 13 submitted
0-to-9 score ballots. I thought I will use it to demonstrate how OllPoll
works.
First, sum up the scores
P1 P2 P3 P4 P5 O1 O2 O3 O4 O5 Y1 Y2 Y3 Y4 Y5
V1 9 7 9 8 9 1 2 1 1 2 0 0 0 0 0
V2 9 8 7 9 9 1 0 1 0 1 0 1 0 1 0
V3 8 9 9 4 8 1 1 2 1 3 1 0 0 1 0
V4 0 0 0 0 0 9 9 8 9 9 0 0 0 0 0
V5 0 0 0 0 0 9 2 7 7 8 0 0 1 0 0
V6 0 0 0 0 0 9 5 8 8 4 0 1 0 0 1
V7 0 0 0 0 0 9 8 8 8 7 0 0 0 0 0
V8 0 0 0 0 0 7 9 9 9 9 0 2 0 0 1
V9 0 0 0 0 0 8 9 9 9 9 0 0 0 0 0
V10 1 1 1 1 1 0 0 0 0 0 9 9 3 9 9
V11 2 1 1 1 0 0 0 0 0 0 8 7 8 8 8
V12 2 2 1 2 2 0 0 0 0 1 9 8 8 9 7
V13 3 0 4 3 2 0 0 0 0 0 9 9 8 8 9
34 28 32 28 31 54 45 53 52 53 36 37 28 36 35
and sort the candidates by scores received
O1 O3 O5 O4 O2 Y2 Y1 Y4 Y5 P1 P3 P5 P2 P4 Y3
V1 1 1 2 1 2 0 0 0 0 9 9 9 7 8 0
V2 1 1 1 0 0 1 0 1 0 9 7 9 8 9 0
V3 1 2 3 1 1 0 1 1 0 8 9 8 9 4 0
V4 9 8 9 9 9 0 0 0 0 0 0 0 0 0 0
V5 9 7 8 7 2 0 0 0 0 0 0 0 0 0 1
V6 9 8 4 8 5 1 0 0 1 0 0 0 0 0 0
V7 9 8 7 8 8 0 0 0 0 0 0 0 0 0 0
V8 7 9 9 9 9 2 0 0 1 0 0 0 0 0 0
V9 8 9 9 9 9 0 0 0 0 0 0 0 0 0 0
V10 0 0 0 0 0 9 9 9 9 1 1 1 1 1 3
V11 0 0 0 0 0 7 8 8 8 2 1 0 1 1 8
V12 0 0 1 0 0 8 9 9 7 2 1 2 2 2 8
V13 0 0 0 0 0 9 9 8 9 3 4 2 0 3 8
54 53 53 52 45 37 36 36 35 34 32 31 28 28 28
Then, on each ballot, strict-stalin-sort the candidates. Keep the ones
with strictly increasing scores, eliminate the rest.
O1 O3 O5 O4 O2 Y2 Y1 Y4 Y5 P1 P3 P5 P2 P4 Y3
V1 1 - 2 - - - - - - 9 - - - - -
V2 1 - - - - - - - - 9 - - - - -
V3 1 2 3 - - - - - - 8 9 - - - -
V4 9 - - - - - - - - - - - - - -
V5 9 - - - - - - - - - - - - - -
V6 9 - - - - - - - - - - - - - -
V7 9 - - - - - - - - - - - - - -
V8 7 9 - - - - - - - - - - - - -
V9 8 9 - - - - - - - - - - - - -
V10 - - - - - 9 - - - - - - - - -
V11 - - - - - 7 8 - - - - - - - -
V12 - - 1 - - 8 9 - - - - - - - -
V13 - - - - - 9 - - - - - - - - -
By how much the scores increase, is the number of votes they get.
O1 O3 O5 O4 O2 Y2 Y1 Y4 Y5 P1 P3 P5 P2 P4 Y3
V1 1 - 1 - - - - - - 7 - - - - -
V2 1 - - - - - - - - 8 - - - - -
V3 1 1 1 - - - - - - 5 1 - - - -
V4 9 - - - - - - - - - - - - - -
V5 9 - - - - - - - - - - - - - -
V6 9 - - - - - - - - - - - - - -
V7 9 - - - - - - - - - - - - - -
V8 7 2 - - - - - - - - - - - - -
V9 8 1 - - - - - - - - - - - - -
V10 - - - - - 9 - - - - - - - - -
V11 - - - - - 7 1 - - - - - - - -
V12 - - 1 - - 7 1 - - - - - - - -
V13 - - - - - 9 - - - - - - - - -
54 4 3 0 0 32 2 0 0 20 1 0 0 0 0
Congratulations, you just converted ballot scores to votes.
O1 gets 54 votes, Y2 gets 32 votes, P1 gets 20 votes, O3 gets 4 votes,
O5 gets 3 votes, Y1 gets 2 votes, and P3 gets 1 vote.
Orange party gets 54 + 4 + 3 = 61 votes (52.6% of seats)
Yellow party gets 32 + 2 = 34 votes (29.3% of seats)
Purple party gets 20 + 1 = 21 votes (18.1% of seats)
I like this score-to-vote method, because it is proportional and
majoritarian at the same time. Thanks to the score ballots you can
support multiple "personal" favorites, but your votes will go to the
"collectively" strongest ones among them.
Cheers,
Oskar
On 6/17/26 09:56, Oskar Stolc via Election-Methods wrote:
> Hi,
>
> inspired by "The space of all proportional voting systems and the most
> majoritarian among them" paper by Speroni di Fenizio and Gewurz, I
> created a score-based system - https://ollpoll.org/about.html
>
> It is a two-pass score-to-vote majoritarian party-list proportional
> representation system and has the following properties:
>
> - score voting based - can score multiple parties and express different
> levels of support
> - eliminates vote splitting (in 2023 parliamentary election in Slovakia
> we had 25 parties to choose from!)
> - assigns votes to the strongest party in each faction, eliminates
> weaker clones from factions. This reduces the number of winning parties,
> thus reduces political fragmentation
> - majoritarian, concentrates power to the strongest parties, but still
> proportionally representative. You can pick any ballot and tell which
> party received how many votes from it
> - if you omit apportionment for seat allocation, you can use it in
> multi-winner elections with huge number of candidates and only a handful
> of winners, like US primaries
>
> As with many things in life, when you invent something, somebody else
> had already invented it before. Is this the case with OllPoll? Do you
> know anything similar, except the paper I mentioned? And most
> importantly, do you find it useful?
>
> Cheers,
> Oskar
> ----
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