Approval Voting is better without runoffs

Most of my research deals with various voting systems and how they can be manipulated by insincere voters.  For many reasons, I think approval voting is the best voting system for single-winner elections.  That's why I have supported The Center for Election Science.  Unfortunately, they've been inconsistent in their proposals for voting reform in different American cities.

Here's a simple example that shows why I don't recommend using runoffs with approval voting:  Say 100 voters are voting in an approval election with a runoff, and they have the following sincere preferences over three candidates A, B and C:

• 45%:  A > B > C
• 20%:  B > C > A
• 35%:  C > B > A

Given these preferences, B would win an A/B runoff, C would win an A/C runoff and B would win a B/C runoff.  A would not win any runoff.  So, if all voters are at least roughly aware of the other preferences and are strategic, we may reasonably assume the following:

• The A>B>C voters want an A/B or B/C runoff.
• The B>C>A voters want an A/B or B/C runoff.
• The C>B>A voters want an A/C runoff.

Therefore, the dominant approval strategies in the general election are

• A>B>C voters:  B only
• B>C>A voters:  B only
• C>B>A voters:  A and C

Then, depending on the runoff rules, either B wins immediately or wins the runoff.  (Voting in the runoff itself is straightforward; insincerity is never rewarded.)  So the sincere Condorcet winner wins the election at equilibrium.  What's wrong with this result?  Well, the required strategy is complicated, which would amplify the power of the most sophisticated voters.  But, more importantly, the best strategies for 80% of the voters turned out to be strongly insincere:  They had to approve one candidate without also approving all candidates they preferred, destroying what is one of approval voting's most desirable properties.

Of course, this reasoning applies equally to range (or score) voting, which is why I don't support STAR voting, though it's certainly better than IRV (often now known as "RCV").

Orioles luckiest again

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last sixteen years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2023:

	nW%	pW%	W%
Braves	.628991	.625206	.641975
Dodgers	.615060	.616491	.617284
Rays	.606959	.615520	.611111
Rangers	.592598	.593753	.555556
Phillies	.574371	.548940	.555556
Twins	.569984	.575368	.537037
Padres	.560562	.567679	.506173
Giants	.555666	.563684	.487654
Astros	.554854	.576969	.555556
Cubs	.547713	.556793	.512346
Orioles	.546171	.579018	.623457
Blue Jays	.544412	.548324	.549383
Brewers	.532569	.553756	.567901
Yankees	.500741	.483319	.506173
Red Sox	.492118	.497636	.481481
Marlins	.488502	.463865	.521739
Tigers	.482595	.448533	.481481
Mariners	.481235	.470466	.543210
Diamondbacks	.478548	.490893	.518519
Mets	.476872	.491154	.459627
Angels	.472545	.447616	.450617
Guardians	.468575	.476447	.469136
Reds	.455652	.478332	.506173
Pirates	.452119	.439700	.469136
Cardinals	.448205	.435237	.438272
Royals	.406154	.392117	.345679
White Sox	.388724	.378256	.376543
Nationals	.385441	.414715	.438272
Rockies	.358665	.373275	.364198
Athletics	.331579	.302274	.308642

So this year the luckiest teams were the Orioles, Mariners and Nationals, and the unluckiest teams were the Giants, Royals and Padres.  In fact, the Orioles finished as the single luckiest team for the second year in a row, but this year they deserved their playoff spot.  If all teams had the win-loss records they deserved, half of the division champions would change:  The Rays would finish ahead of the Orioles, the Rangers would finish ahead of the Astros and the Cubs would finish ahead of the Brewers.  If the twelve actually best teams had made the playoffs, the Padres, Giants and Cubs would be in and the Brewers, Marlins and Diamondbacks would be out.  The Braves were a bit lucky to win so many games, but they indeed deserved the best record in baseball.

Based on the above results, it's reasonable to predict:

	Twins over Astros	Rays over Twins	Braves over Rays
Twins over Blue Jays
Rays over Rangers	Rays over Orioles
	Dodgers over Brewers	Braves over Dodgers
Brewers over Diamondbacks
Phillies over Marlins	Braves over Phillies

But what I'm rooting for would give us a rematch of the 1993 Series:

	Blue Jays over Astros	Blue Jays over Rangers	Blue Jays over Phillies
Blue Jays over Twins
Rangers over Rays	Rangers over Orioles
	Brewers over Dodgers	Phillies over Brewers
Brewers over Diamondbacks
Phillies over Marlins	Phillies over Braves

I got all the statistics I needed for this analysis from these three pages: A B C

Dodgers and Astros continue excellence

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last fifteen years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2022:

	nW%	pW%	W%
Dodgers	.697697	.714554	.685185
Astros	.660354	.655946	.654321
Yankees	.639752	.656092	.611111
Braves	.621624	.616300	.623457
Mets	.582821	.608986	.623457
Blue Jays	.568327	.560207	.567901
Cardinals	.562958	.587043	.574074
Phillies	.550545	.539558	.537037
Guardians	.541168	.543885	.567901
Brewers	.540217	.523947	.530864
Padres	.537667	.530139	.549383
Rays	.527732	.537124	.530864
Mariners	.525782	.546596	.555556
Twins	.518329	.507956	.481481
Giants	.505139	.512302	.500000
Angels	.499028	.468136	.450617
White Sox	.487367	.479790	.500000
Red Sox	.482221	.468767	.481481
Rangers	.466922	.477294	.419753
Orioles	.465776	.490595	.512346
Diamondbacks	.453840	.475901	.456790
Cubs	.452090	.451326	.456790
Marlins	.422251	.435005	.425926
Rockies	.414243	.399056	.419753
Royals	.395013	.393867	.401235
Tigers	.391875	.388919	.407407
Reds	.386796	.396609	.382716
Pirates	.379282	.356039	.382716
Nationals	.376609	.345471	.339506
Athletics	.347303	.364285	.370370

So this year the luckiest teams were the Orioles, Mets and Mariners, and the unluckiest teams were the Angels, Rangers and Nationals.  This year, Nostradamian win percentage correlated highly with actual win percentage:  If all teams had the win-loss records they deserved, none of the division champions would change.  If the twelve actually best teams had made the playoffs, the Brewers would be in and the Mariners would be out.  The Yankees get much of the attention, and the Athletics pioneered analytics, but the Dodgers and Astros are clearly the modern baseball dynasties.

Based on the above results, it's reasonable to predict:

	Astros over Blue Jays	Astros over Yankees	Dodgers over Astros
Blue Jays over Mariners
Guardians over Rays	Yankees over Guardians
	Braves over Cardinals	Dodgers over Braves
Cardinals over Phillies
Mets over Padres	Dodgers over Mets

But what I'm rooting for would give us a rematch of the 1993 Series:

	Blue Jays over Astros	Blue Jays over Guardians	Blue Jays over Phillies
Blue Jays over Mariners
Guardians over Rays	Guardians over Yankees
	Phillies over Braves	Phillies over Padres
Phillies over Cardinals
Padres over Mets	Padres over Dodgers

I got all the statistics I needed for this analysis from these three pages: A B C

Best Blue Jays team since 2015

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last fourteen years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2021:

	nW%	pW%	W%
Dodgers	.658826	.671906	.654321
Giants	.635012	.635058	.660494
Astros	.615526	.621593	.586420
Blue Jays	.597655	.609700	.561728
White Sox	.595228	.601244	.574074
Rays	.588671	.623192	.617284
Brewers	.572128	.576885	.586420
Braves	.565929	.584226	.546584
Yankees	.550275	.527828	.567901
Red Sox	.528498	.546295	.567901
Cardinals	.526901	.522565	.555556
Athletics	.510203	.535789	.530864
Padres	.509499	.513369	.487654
Reds	.504500	.515385	.512346
Phillies	.499604	.493195	.506173
Mets	.498352	.477557	.475309
Nationals	.479903	.443281	.401235
Indians	.471884	.493664	.493827
Twins	.469998	.438748	.450617
Angels	.461637	.451570	.475309
Rockies	.459213	.466059	.459627
Mariners	.450767	.467737	.555556
Tigers	.448364	.462894	.475309
Marlins	.444847	.446241	.413580
Royals	.437805	.436919	.456790
Cubs	.422376	.421055	.438272
Rangers	.391132	.380896	.370370
Diamondbacks	.380847	.377222	.320988
Pirates	.373419	.360502	.376543
Orioles	.371278	.336078	.320988

So this year the luckiest team was the Mariners, and it wasn't close; they ended up almost sneaking into the playoffs with a 90–72 record even though they deserved a record closer to 73–89.  The unluckiest teams were the Nationals, Diamondbacks and Orioles, but the unluckiest good team was the Blue Jays, who only finished fourth in the AL East even though they were really the fourth-best team in baseball.  If all teams had the win-loss records they deserved, just two of the division champions would change:  The Blue Jays would finish 2 games ahead of the Rays (and 8 games ahead of the Yankees) and the Dodgers would finish 4 games ahead of the Giants.  If the ten actually best teams had made the playoffs, the Blue Jays would be in and the Cardinals would be out.

Based on the above results, it's reasonable to predict:

	Rays over Yankees	Astros over Rays	Dodgers over Astros
Yankees over Red Sox
	Astros over White Sox
	Brewers over Braves	Dodgers over Brewers
Dodgers over Cardinals	Dodgers over Giants

But what I'm rooting for is very different:

	Red Sox over Rays	Red Sox over Astros	Red Sox over Cardinals
Red Sox over Yankees
	Astros over White Sox
	Brewers over Braves	Cardinals over Brewers
Cardinals over Dodgers	Cardinals over Giants

I got all the statistics I needed for this analysis from these three pages: A B C

Lucky Florida teams

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last thirteen years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2020:

	nW%	pW%	W%
Dodgers	0.713753	0.711692	0.716667
Padres	0.617547	0.633491	0.616667
Braves	0.608826	0.585723	0.583333
White Sox	0.596763	0.598544	0.583333
Twins	0.581751	0.601101	0.600000
Yankees	0.578828	0.570060	0.550000
Rays	0.573901	0.604882	0.666667
Giants	0.560897	0.503070	0.483333
Indians	0.543751	0.577642	0.583333
Reds	0.543271	0.500000	0.516667
Angels	0.527212	0.459890	0.433333
Mets	0.526750	0.466147	0.433333
Athletics	0.525733	0.575541	0.600000
Brewers	0.515599	0.469586	0.483333
Orioles	0.509350	0.467813	0.416667
Cardinals	0.505368	0.521451	0.517241
Cubs	0.499782	0.545210	0.566667
Astros	0.490059	0.506606	0.483333
Blue Jays	0.479987	0.485101	0.533333
Phillies	0.474304	0.492585	0.466667
Royals	0.457575	0.457840	0.433333
Nationals	0.440515	0.487679	0.433333
Red Sox	0.417903	0.416592	0.400000
Mariners	0.403726	0.419991	0.450000
Marlins	0.394620	0.434106	0.516667
Diamondbacks	0.389136	0.457889	0.416667
Rockies	0.386206	0.387711	0.433333
Tigers	0.382194	0.389928	0.396552
Pirates	0.375709	0.362696	0.316667
Rangers	0.369462	0.352885	0.366667

So this year the luckiest teams were the Marlins and Rays; the unluckiest were the Angels, Mets and Orioles.  The Giants didn't make it into the 16-team playoffs despite being the eighth-best team in baseball; the Marlins made it in despite being the sixth-worst team in baseball.  Unpredictability is amplified with such a short season, and the playoffs will be more chaotic than usual with so many teams.

Based on the above results, it's reasonable to predict:

Athletics over Astros	White Sox over Athletics	White Sox over Yankees	Dodgers over White Sox
White Sox over Twins
Yankees over Indians	Yankees over Rays
Rays over Blue Jays
Cubs over Marlins	Braves over Cubs	Dodgers over Braves
Braves over Reds
Padres over Cardinals	Dodgers over Padres
Dodgers over Brewers

But what I'm rooting for is very different:

Athletics over Astros	Athletics over Twins	Blue Jays over Athletics	Blue Jays over Reds
Twins over White Sox
Indians over Yankees	Blue Jays over Indians
Blue Jays over Rays
Cubs over Marlins	Reds over Cubs	Reds over Padres
Reds over Braves
Padres over Cardinals	Padres over Brewers
Brewers over Dodgers

I got all the statistics I needed for this analysis from these three pages: A B C

Astros and Dodgers best again

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last twelve years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2019:

	nW%	pW%	W%
Astros	.677502	.660185	.660494
Dodgers	.670291	.662417	.654321
Twins	.598220	.599059	.623457
Rays	.593823	.572202	.592593
Yankees	.576377	.609711	.635802
Nationals	.574007	.584791	.574074
Athletics	.571746	.598100	.598765
Red Sox	.551824	.538578	.518519
Braves	.547440	.563884	.598765
Cubs	.545871	.557790	.518519
Indians	.544647	.571520	.574074
Mets	.534406	.532305	.530864
Cardinals	.532302	.565188	.561728
Brewers	.524753	.501788	.549383
Reds	.514368	.493520	.462963
Diamondbacks	.511116	.541098	.524691
Padres	.467561	.433718	.432099
Phillies	.463987	.488331	.500000
Angels	.458322	.444822	.444444
Mariners	.444125	.425571	.419753
Giants	.439959	.440293	.475309
Rockies	.437650	.437461	.438272
Rangers	.435699	.463187	.481481
Blue Jays	.435260	.440144	.413580
White Sox	.423228	.426697	.447205
Pirates	.419484	.416669	.425926
Royals	.390277	.396650	.364198
Marlins	.385985	.377663	.351852
Orioles	.379034	.367415	.333333
Tigers	.344497	.304070	.291925

So this year the luckiest teams were the Yankees, Braves and Rangers; the unluckiest were the Tigers, Reds and Orioles.  Only two of the best eight teams were from the National League.  Only the seven actually best teams made the playoffs; if the ten actually best teams had made the playoffs, the Red Sox and Cubs would be in and the Cardinals and Brewers would be out.  If all teams had the win-loss records they deserved, half of the division champions would change:  The Rays would finish 3 games ahead of the Yankees, the Nationals would finish 4 games ahead of the Braves and the Cubs would finish 2 games ahead of the Cardinals.  The Astros had the best record in baseball and deserved it; The Tigers had the worst record in baseball and deserved it.

Based on the above results, it's reasonable to predict:

	Astros over Rays	Astros over Twins	Astros over Dodgers
Rays over Athletics
	Twins over Yankees
	Braves over Cardinals	Dodgers over Braves
Nationals over Brewers	Dodgers over Nationals

But what I'm rooting for is very different:

	Athletics over Astros	Athletics over Twins	Athletics over Cardinals
Athletics over Rays
	Twins over Yankees
	Cardinals over Braves	Cardinals over Brewers
Brewers over Nationals	Brewers over Dodgers

I got all the statistics I needed for this analysis from these three pages: A B C

Repeat of last year's World Series?

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last eleven years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2018:

	nW%	pW%	W%
Astros	.642414	.675428	.635802
Dodgers	.628896	.623713	.564417
Red Sox	.609712	.635185	.666667
Yankees	.599109	.608342	.617284
Athletics	.582831	.584950	.598765
Rays	.572413	.546929	.555556
Indians	.567910	.604999	.561728
Brewers	.562571	.561301	.588957
Braves	.561871	.565644	.555556
Nationals	.552453	.555882	.506173
Cubs	.552293	.575090	.582822
Cardinals	.524177	.542837	.543210
Rockies	.522768	.520991	.558282
Diamondbacks	.512143	.533499	.506173
Mariners	.496427	.477597	.549383
Pirates	.493447	.499339	.509317
Mets	.490566	.479498	.475309
Angels	.486871	.499366	.493827
Phillies	.485483	.466821	.493827
Twins	.465049	.477634	.481481
Blue Jays	.446514	.427329	.450617
Reds	.441841	.426094	.413580
Giants	.431721	.432821	.450617
Padres	.423482	.401735	.407407
Rangers	.419389	.436166	.413580
White Sox	.418987	.384664	.382716
Tigers	.404777	.394604	.395062
Royals	.385066	.380352	.358025
Marlins	.379331	.358750	.391304
Orioles	.351535	.340793	.290123

So this year the luckiest teams were the Red Sox, Mariners and Rockies; the unluckiest were the Dodgers, Orioles and Nationals.  Only one of the best seven teams was from the National League.  Only the five actually best teams made the playoffs; if the ten actually best teams had made the playoffs, the Rays and Nationals would be in and the Cubs and Rockies would be out.  If all teams had the win-loss records they deserved, no division champions would change—in fact, there'd be only one minor change in the final positions:  The White Sox would finish 2 games ahead of the Tigers instead of 2 games behind them in the AL Central.  The Nationals would take the wild card ahead of the Rockies.  Because of divisional alignments, the Rays still wouldn't make the playoffs despite being better than the Indians.  And the Astros, not the Red Sox, would have the best record in baseball and home-field advantage throughout the postseason.

Based on the above results, it's reasonable to predict:

	Red Sox over Yankees	Astros over Red Sox	Astros over Dodgers
Yankees over Athletics
	Astros over Indians
	Dodgers over Braves	Dodgers over Brewers
Cubs over Rockies	Brewers over Cubs

But what I'm rooting for is very different:

	Athletics over Red Sox	Athletics over Indians	Athletics over Cubs
Athletics over Yankees
	Indians over Astros
	Dodgers over Braves	Cubs over Dodgers
Cubs over Rockies	Cubs over Brewers

I got all the statistics I needed for this analysis from these three pages: A B C

Finally the Indians' turn?

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last ten years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2017:

	nW%	pW%	W%
Indians	.644021	.663830	.629630
Yankees	.623690	.617778	.561728
Dodgers	.620897	.626809	.641975
Astros	.609607	.611056	.623457
Nationals	.593533	.589530	.598765
Diamondbacks	.577449	.594370	.574074
Cubs	.572111	.576184	.567901
Cardinals	.536145	.534912	.512346
Red Sox	.534914	.573306	.574074
Rays	.532958	.493455	.493827
Rockies	.512520	.538722	.537037
Brewers	.511367	.522400	.530864
Twins	.501663	.515408	.524691
Mariners	.493556	.486776	.481481
Athletics	.492554	.449257	.462963
Marlins	.479785	.474852	.475309
Rangers	.472678	.490369	.481481
Angels	.466345	.500645	.493827
Blue Jays	.456683	.443793	.469136
Braves	.453302	.447697	.444444
Royals	.450858	.445607	.493827
Reds	.449607	.434823	.419753
Mets	.446459	.427075	.432099
Phillies	.439353	.442987	.407407
Orioles	.438031	.443559	.462963
Tigers	.430429	.411352	.395062
Pirates	.430112	.458861	.462963
White Sox	.426643	.431942	.413580
Giants	.408797	.412056	.395062
Padres	.401517	.365740	.438272

So this year the luckiest teams were the Royals, Red Sox and Padres; the unluckiest were the Yankees, Rays and Tigers.  The seven actually best teams made the playoffs; if the ten actually best teams had made the playoffs, the Cardinals and Rays would be in and the Twins and Rockies would be out.  If all teams had the win-loss records they deserved, only one division champion would change:  The Yankees would finish about 14 games ahead of the Red Sox instead of 2 games behind.  The Royals would be 73–89 instead of 80–82, but would still finish in third place in the AL Central; the Athletics would move from last to 3rd and the Angels would move from 2nd to last in the AL West.  And the Indians, not the Dodgers, would have the best record in baseball and home-field advantage throughout the postseason.

Based on the above results, it's reasonable to predict:

	Indians over Yankees	Indians over Astros	Indians over Dodgers
Yankees over Twins
	Astros over Red Sox
	Nationals over Cubs	Dodgers over Nationals
Diamondbacks over Rockies	Dodgers over Diamondbacks

But here's what I'm rooting for:

	Indians over Twins	Red Sox over Indians	Cubs over Red Sox
Twins over Yankees
	Red Sox over Astros
	Cubs over Nationals	Cubs over Rockies
Rockies over Diamondbacks	Rockies over Dodgers

I got all the statistics I needed for this analysis from these three pages: A B C

Year of the Cub

Predicting the baseball postseason is an annual tradition on this otherwise defunct blog, so, as busy as I am, I'll take a few minutes to do the same kind of analysis I've done the last nine years, essentially factoring out each team's luck to see how good they really were this season.  The Nostradamian, Pythagorean and actual win percentages for all teams in 2016:

	nW%	pW%	W%
Cubs	.668397	.664640	.639752
Red Sox	.621439	.605962	.574074
Nationals	.592000	.599543	.586420
Dodgers	.570874	.558219	.561728
Blue Jays	.566575	.559517	.549383
Indians	.555688	.563363	.583851
Giants	.554156	.556929	.537037
Cardinals	.549562	.541052	.530864
Tigers	.535488	.518033	.534161
Mets	.531894	.538309	.537037
Mariners	.521023	.537790	.530864
Orioles	.510273	.518181	.549383
Rockies	.502655	.491951	.462963
Astros	.500817	.514765	.518519
Rangers	.489922	.504809	.586420
Rays	.489653	.472932	.419753
Yankees	.489244	.485437	.518519
Marlins	.487651	.481528	.490683
White Sox	.477393	.481066	.481481
Brewers	.465970	.459656	.450617
Pirates	.459386	.482161	.484472
Braves	.453149	.417239	.422360
Royals	.448659	.475605	.500000
Athletics	.447134	.430431	.425926
Angels	.444426	.493664	.456790
Diamondbacks	.437592	.423523	.425926
Twins	.428857	.405941	.364198
Padres	.413678	.447349	.419753
Reds	.405368	.420057	.419753
Phillies	.396215	.380592	.438272

So this year the luckiest teams were the Rangers, Royals, Phillies and Orioles; the unluckiest were the Rays, Twins and Red Sox.  The seven actually best teams made the playoffs; if the ten actually best teams had made the playoffs, the Cardinals and Tigers would be in and the Orioles and Rangers would be out.  The Cubs won 103 games but deserved to win 108, more than they've won in a season since before they won the World Series.  Five teams better than the Rangers will be watching the playoffs at home; for the second year in a row, they've won the AL West despite deserving a losing record.  If a team's winning more games than their statistics would predict is evidence of superior managing, then Jeff Banister must be one of the best managers in baseball.

Based on the above results, it's reasonable to predict:

	Blue Jays over Rangers	Red Sox over Blue Jays	Cubs over Red Sox
Blue Jays over Orioles
	Red Sox over Indians
	Nationals over Dodgers	Cubs over Nationals
Giants over Mets	Cubs over Giants

But what I'm rooting for is a little different:

	Blue Jays over Rangers	Blue Jays over Red Sox	Blue Jays over Cubs
Blue Jays over Orioles
	Red Sox over Indians
	Dodgers over Nationals	Cubs over Dodgers
Mets over Giants	Cubs over Mets

I got all the statistics I needed for this analysis from these three pages: A B C

All the way, Jays!