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Highest averages method
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=== Example: Jefferson ===<!-- Excel spreadsheet for calculations: https://onedrive.live.com/embed?resid=1B54A1377C25E2F3%21112&authkey=%21AOsVPs31hRuqsX0&em=2&AllowTyping=True&ActiveCell=%27Jefferson%27!F3&wdHideGridlines=True&wdHideHeaders=True&wdDownloadButton=True&wdInConfigurator=True&wdInConfigurator=True --> The following example shows how Jefferson's method can differ substantially from less-biased methods such as Webster. In this election, the largest party wins 46% of the vote, but takes 52.5% of the seats, enough to win a majority outright against a coalition of all other parties (which together reach 54% of the vote). Moreover, it does this in violation of quota: the largest party is entitled only to 9.7 seats, but it wins 11 regardless. The largest congressional district is nearly twice the size of the smallest district. The Webster method shows none of these properties, with a maximum error of 22.6%. {| class="wikitable mw-collapsible" style="text-align:center; color:#000000;" |+ ! colspan="7" style="vertical-align:bottom; background-color:#ffffff;" |Jefferson ! style="background-color:#ffffff; font-weight:normal; text-align:left;" | ! colspan="7" style="background-color:#FFF;" |Webster |- style="font-weight:bold;" ! style="vertical-align:bottom;" |Party ! style="vertical-align:bottom;" |Yellow ! style="vertical-align:bottom;" |White ! style="vertical-align:bottom;" |Red ! style="vertical-align:bottom;" |Green ! style="vertical-align:bottom;" |Purple ! style="vertical-align:bottom;" |Total | rowspan="6" style="background-color:#ffffff; font-weight:normal; text-align:left;" | !Party !Yellow !White !Red !Green !Purple !Total |- ! style="vertical-align:bottom; font-weight:bold;" |Votes | style="vertical-align:bottom; text-align:left;" |46,000 | style="vertical-align:bottom;" |25,100 | style="vertical-align:bottom;" |12,210 | style="vertical-align:bottom;" |8,350 | style="vertical-align:bottom;" |8,340 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |100,000 ! style="font-weight:bold;" |Votes | style="text-align:left;" |46,000 |25,100 |12,210 |8,350 |8,340 | style="text-align:right; font-weight:bold;" |100,000 |- style="text-align:left;" ! style="text-align:center; vertical-align:bottom; font-weight:bold;" |Seats | style="vertical-align:bottom;" |11 | style="vertical-align:bottom;" |6 | style="vertical-align:bottom;" |2 | style="vertical-align:bottom;" |1 | style="vertical-align:bottom;" |1 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |21 ! style="text-align:center; font-weight:bold;" |Seats |9 |5 |3 |2 |2 | style="text-align:right; font-weight:bold;" |21 |- style="text-align:left;" ! style="text-align:center; vertical-align:bottom; font-weight:bold;" |Ideal | style="vertical-align:bottom;" |9.660 | style="vertical-align:bottom;" |5.271 | style="vertical-align:bottom;" |2.564 | style="vertical-align:bottom;" |1.754 | style="vertical-align:bottom;" |1.751 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |21 ! style="text-align:center; font-weight:bold;" |Ideal |9.660 |5.271 |2.564 |1.754 |1.751 | style="text-align:right; font-weight:bold;" |21 |- style="text-align:left;" ! style="text-align:center; vertical-align:bottom; font-weight:bold;" |Votes/Seat | style="vertical-align:bottom;" |4182 | style="vertical-align:bottom;" |4183 | style="vertical-align:bottom;" |6105 | style="vertical-align:bottom;" |8350 | style="vertical-align:bottom;" |8340 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |4762 ! style="text-align:center; font-weight:bold;" |Votes/Seat |5111 |5020 |4070 |4175 |4170 | style="text-align:right; font-weight:bold;" |4762 |- style="text-align:left;" ! style="text-align:center; vertical-align:bottom; font-weight:bold;" |% Error | style="vertical-align:bottom;" |13.0% | style="vertical-align:bottom;" |13.0% | style="vertical-align:bottom;" | -24.8% | style="vertical-align:bottom;" | -56.2% | style="vertical-align:bottom;" | -56.0% | style="text-align:right; vertical-align:bottom; font-weight:bold;" |(100.%) ! style="text-align:center; font-weight:bold;" |(% Range) | -7.1% | -5.3% |15.7% |13.2% |13.3% | style="text-align:right; font-weight:bold;" |(22.6%) |- style="font-weight:bold;" ! style="vertical-align:bottom;" |Seats ! colspan="5" |Averages ! style="vertical-align:bottom;" |Signposts | style="background-color:#ffffff; font-weight:normal; text-align:left;" | !Seats ! colspan="5" |Averages !Signposts |- ! style="vertical-align:bottom; font-weight:bold;" |1 | style="vertical-align:bottom; background-color:#63BE7B;" |46,000 | style="vertical-align:bottom; background-color:#AADBB8;" |25,100 | style="vertical-align:bottom; background-color:#D6EDDE;" |12,210 | style="vertical-align:bottom; background-color:#E3F2E9;" |8,350 | style="vertical-align:bottom; background-color:#E3F2E9;" |8,340 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |1.00 | rowspan="11" style="background-color:#ffffff; text-align:left;" | ! style="font-weight:bold;" |1 | style="background-color:#63BE7B;" |92,001 | style="background-color:#AADBB8;" |50,201 | style="background-color:#D5ECDD;" |24,420 | style="background-color:#E2F2E8;" |16,700 | style="background-color:#E2F2E9;" |16,680 | style="text-align:right; font-weight:bold;" |0.50 |- ! style="vertical-align:bottom; font-weight:bold;" |2 | style="vertical-align:bottom; background-color:#B1DEBF;" |23,000 | style="vertical-align:bottom; background-color:#D5ECDD;" |12,550 | style="vertical-align:bottom; background-color:#EAF5F0;" |6,105 | style="vertical-align:bottom;" |4,175 | style="vertical-align:bottom;" |4,170 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |2.00 ! style="font-weight:bold;" |2 | style="background-color:#CAE8D4;" |30,667 | style="background-color:#E2F2E8;" |16,734 | style="background-color:#F0F8F5;" |8,140 | style="background-color:#F4F9F9;" |5,567 | style="background-color:#F5F9F9;" |5,560 | style="text-align:right; font-weight:bold;" |1.50 |- ! style="vertical-align:bottom; font-weight:bold;" |3 | style="vertical-align:bottom; background-color:#CBE9D5;" |15,333 | style="vertical-align:bottom; background-color:#E3F2E9;" |8,367 | style="vertical-align:bottom;" |4,070 | style="vertical-align:bottom;" |2,783 | style="vertical-align:bottom;" |2,780 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |3.00 ! style="font-weight:bold;" |3 | style="background-color:#DFF1E6;" |18,400 | style="background-color:#EDF6F2;" |10,040 | style="background-color:#F6FAFA;" |4,884 |3,340 |3,336 | style="text-align:right; font-weight:bold;" |2.50 |- ! style="vertical-align:bottom; font-weight:bold;" |4 | style="vertical-align:bottom; background-color:#D8EEE0;" |11,500 | style="vertical-align:bottom; background-color:#EAF5EF;" |6,275 | style="vertical-align:bottom;" |3,053 | style="vertical-align:bottom;" |2,088 | style="vertical-align:bottom;" |2,085 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |4.00 ! style="font-weight:bold;" |4 | style="background-color:#E8F4EE;" |13,143 | style="background-color:#F2F8F6;" |7,172 |3,489 |2,386 |2,383 | style="text-align:right; font-weight:bold;" |3.50 |- ! style="vertical-align:bottom; font-weight:bold;" |5 | style="vertical-align:bottom; background-color:#E0F1E7;" |9,200 | style="vertical-align:bottom; background-color:#EEF7F3;" |5,020 | style="vertical-align:bottom;" |2,442 | style="vertical-align:bottom;" |1,670 | style="vertical-align:bottom;" |1,668 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |5.00 ! style="font-weight:bold;" |5 | style="background-color:#EDF6F2;" |10,222 | style="background-color:#F4F9F9;" |5,578 |2,713 |1,856 |1,853 | style="text-align:right; font-weight:bold;" |4.50 |- ! style="vertical-align:bottom; font-weight:bold;" |6 | style="vertical-align:bottom; background-color:#E5F3EB;" |7,667 | style="vertical-align:bottom; background-color:#F1F8F6;" |4,183 | style="vertical-align:bottom;" |2,035 | style="vertical-align:bottom;" |1,392 | style="vertical-align:bottom;" |1,390 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |6.00 ! style="font-weight:bold;" |6 | style="background-color:#F0F7F5;" |8,364 | style="background-color:#F6FAFA;" |4,564 |2,220 |1,518 |1,516 | style="text-align:right; font-weight:bold;" |5.50 |- ! style="vertical-align:bottom; font-weight:bold;" |7 | style="vertical-align:bottom; background-color:#E9F5EF;" |6,571 | style="vertical-align:bottom;" |3,586 | style="vertical-align:bottom;" |1,744 | style="vertical-align:bottom;" |1,193 | style="vertical-align:bottom;" |1,191 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |7.00 ! style="font-weight:bold;" |7 | style="background-color:#F2F8F6;" |7,077 |3,862 |1,878 |1,285 |1,283 | style="text-align:right; font-weight:bold;" |6.50 |- ! style="vertical-align:bottom; font-weight:bold;" |8 | style="vertical-align:bottom; background-color:#ECF6F1;" |5,750 | style="vertical-align:bottom;" |3,138 | style="vertical-align:bottom;" |1,526 | style="vertical-align:bottom;" |1,044 | style="vertical-align:bottom;" |1,043 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |8.00 ! style="font-weight:bold;" |8 | style="background-color:#F4F9F8;" |6,133 |3,347 |1,628 |1,113 |1,112 | style="text-align:right; font-weight:bold;" |7.50 |- ! style="vertical-align:bottom; font-weight:bold;" |9 | style="vertical-align:bottom; background-color:#EEF7F3;" |5,111 | style="vertical-align:bottom;" |2,789 | style="vertical-align:bottom;" |1,357 | style="vertical-align:bottom;" |928 | style="vertical-align:bottom;" |927 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |9.00 ! style="font-weight:bold;" |9 | style="background-color:#F5F9F9;" |5,412 |2,953 |1,436 |982 |981 | style="text-align:right; font-weight:bold;" |8.50 |- ! style="vertical-align:bottom; font-weight:bold;" |10 | style="vertical-align:bottom; background-color:#F0F7F4;" |4,600 | style="vertical-align:bottom;" |2,510 | style="vertical-align:bottom;" |1,221 | style="vertical-align:bottom;" |835 | style="vertical-align:bottom;" |834 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |10.00 ! style="font-weight:bold;" |10 | style="background-color:#F6FAFA;" |4,842 |2,642 |1,285 |879 |878 | style="text-align:right; font-weight:bold;" |9.50 |- ! style="vertical-align:bottom; font-weight:bold;" |11 | style="vertical-align:bottom; background-color:#F1F8F6;" |4,182 | style="vertical-align:bottom;" |2,282 | style="vertical-align:bottom;" |1,110 | style="vertical-align:bottom;" |759 | style="vertical-align:bottom;" |758 | style="text-align:right; vertical-align:bottom; font-weight:bold;" |11.00 ! style="font-weight:bold;" |11 | style="background-color:#F6FAFA;" |4,381 |2,391 |1,163 |795 |794 | style="text-align:right; font-weight:bold;" |10.50 |}
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