DemoChoice Web Poll: Hill test elections 
3 candidates will be elected with 598 ballots cast. 
First Round 
Next Round  Final Round  Depth 
Slices  How it works 
Main Page
Round 1 
Votes 

149 ^{31}/_{60} (25%)


Max 
A 
400  
(66.9%) 

1 
D 
198  
(33.1%) 

1 
   


Results 

  A 
Elected   
D 
Elected   

  


Transfers (to these colors): 

 
Transfers (from these colors): 

 
   


Histograms

Surplus

New Max

Votes: Ballots


A 
250  ^{29}/_{60} 
^{23}/_{60} 
 
D 
48  ^{29}/_{60} 
^{46}/_{60} 
 

Each ballot initially counts toward its highestranked eligible choice. However, in future rounds, a maximum fraction of a ballot may be imposed on a candidate. This allows voters for popular winners (or for eliminated losers) to help unelected candidates or candidates elected later. If there are no such candidates, the leftover fraction goes back to the first winner, or count toward "none of these" if there are no ranked winners.
The ballot fraction precision is equal to 1/Seats(Seats+1), which ensures that winners can always be kept between Enough votes to win, more than (Total Votes for Candidates)/(Seats+1),
and the Ideal Number of votes, (Total Votes for Candidates)/Seats.
If all winners have at least "Enough" votes, it is impossible to elect too many candidates. This number is Ballots/(Seats+1) plus the smallest fraction.
If all winners have exactly the Ideal Number of votes, and they each have an equal voice, everyone who voted for a winner is equally represented.
The dotted line on the graph represents Enough votes.
The histogram shows how many ballots count a given fraction of a vote toward a winner. It is used to determine how much to lower the maximum.
Ballots that cannot count for a lowerranked candidate are not included in the histogram.
The maximum is reduced in steps of the defined fractional precision, reducing the surplus by the number of ballots in the affected histogram bins divided by that precision.
This process stops just before too many would be transferred. At this point, the affected bins are shown in red.
When only winners remain, they may reduce their maxima toward the Ideal Number.
Go to the next round
DemoChoice Web Poll: Hill test elections 
3 candidates will be elected with 598 ballots cast. 
First Round 
Next Round  Final Round  Previous Round  Depth 
Slices  How it works 
Main Page
Round 2 
Votes 

149 ^{31}/_{60} (25%)


Max 
A 
153  ^{20}/_{60} 
(25.6%) 

^{23}/_{60} 
D 
151  ^{48}/_{60} 
(25.4%) 

^{46}/_{60} 
B 
246  ^{40}/_{60} 
(41.2%) 

1 
E 
46  ^{12}/_{60} 
(7.7%) 

1 
   


Results 

  B 
Elected   
   


Histograms

Surplus

New Max

Votes: Ballots


B 
97  ^{9}/_{60} 
1 
 

The histogram shows how many ballots count a given fraction of a vote toward a winner. It is used to determine how much to lower the maximum.
Ballots that cannot count for a lowerranked candidate are not included in the histogram.
The maximum is reduced in steps of the defined fractional precision, reducing the surplus by the number of ballots in the affected histogram bins divided by that precision.
This process stops just before too many would be transferred. At this point, the affected bins are shown in red.
When only winners remain, they may reduce their maxima toward the Ideal Number.
There is a newly elected candidate whose maximum could not be reduced.
The surplus is lower than the number of ballots in the first histogram bin (the ballots counting the largest fraction toward the candidate) times the smallest fraction,
so they cannot all transfer that fraction without exceeding the surplus.
Go to the next round
DemoChoice Web Poll: Hill test elections 
3 candidates will be elected with 598 ballots cast. 
First Round 
Next Round  Final Round  Previous Round  Depth 
Slices  How it works 
Main Page
Round 3 
Votes 

149 ^{31}/_{60} (25%)


Max 
A 
153  ^{20}/_{60} 
(25.6%) 

^{23}/_{60} 
D 
151  ^{48}/_{60} 
(25.4%) 

^{46}/_{60} 
B 
246  ^{40}/_{60} 
(41.2%) 

1 
E 
46  ^{12}/_{60} 
(7.7%) 

1 
   


Results 

  E 
Defeated   

  


Transfers (to these colors): 

 
   



No elected candidates could reduce their maxima, so candidates were eliminated instead.
The lastplace candidate is eliminated.
Go to the next round
DemoChoice Web Poll: Hill test elections 
3 candidates will be elected with 598 ballots cast. 
First Round 
Next Round  Final Round  Previous Round  Depth 
Slices  How it works 
Main Page
Round 4 
Votes 

199 ^{20}/_{60} (33.3%)


Max 
A 
153  ^{20}/_{60} 
(25.6%) 

^{23}/_{60} 
D 
198  
(33.1%) 

^{46}/_{60} 
B 
246  ^{40}/_{60} 
(41.2%) 

1 
   


Results 

  B 
Equalized   
   


Histograms

Surplus

New Max

Votes: Ballots


B 
47  ^{20}/_{60} 
0 
 

The histogram shows how many ballots count a given fraction of a vote toward a winner. It is used to determine how much to lower the maximum.
Ballots that cannot count for a lowerranked candidate are not included in the histogram.
The maximum is reduced in steps of the defined fractional precision, reducing the surplus by the number of ballots in the affected histogram bins divided by that precision.
This process stops just before too many would be transferred. At this point, the affected bins are shown in red.
When only winners remain, they may reduce their maxima toward the Ideal Number.
Only winners remain, so the dotted line is raised to the Ideal Number.
Go to the next round
DemoChoice Web Poll: Hill test elections 
3 candidates will be elected with 598 ballots cast. 
First Round 
Final Round  Previous Round  Depth 
Slices  How it works 
Main Page
Round 5 
Votes 

199 ^{20}/_{60} (33.3%)


Max 
A 
153  ^{20}/_{60} 
(25.6%) 

^{23}/_{60} 
D 
198  
(33.1%) 

^{46}/_{60} 
B 
246  ^{40}/_{60} 
(41.2%) 

0 
   


Results 
  


A  Elected    B  Elected    D  Elected   
   



No further maximum reductions are allowed, so the count is complete. All winners should be near the Ideal Number of votes.
Usually most ballots count toward their highestranked winner. Some count for two winners, but rarely more than that.
See the slice report. The depth report shows the contribution of lower choices to the result.
The "none of these" pile is an accurate measure of unsatisfied voters.
DemoChoice Web Poll: Hill test elections 
3 candidates will be elected with 598 ballots cast. 
First Round 
Final Round 
Depth 
Slices  How it works 
Main Page
Ballot Depth: This shows how much the lower rankings on ballots contributed to the winning
candidates.
Rank 
Fraction of votes for winners 
1st  58.8% 

2nd  41.2% 

DemoChoice Web Poll: Hill test elections 
3 candidates will be elected with 598 ballots cast. 
First Round 
Final Round 
Depth 
Slices 
How it works 
Main Page
Slices: This shows the distribution of how many winners a ballot counted for.
Slices 
Percentage of ballots with that many slices 
1  33.1% 

2  66.9% 
