tweak degree of injected uncertainty: reduce it overall & in non-battleground states

README.md

@@ -79,11 +79,11 @@ However, this 95% really doesn't feel right. It is only accounting, and very nai
 
 ### The adjusted polls story 
 
-If we look at how [Gallup presidential election polls](https://news.gallup.com/poll/110548/gallup-presidential-election-trial-heat-trends.aspx) did between 1936 and 2008, we get a sense that polls in mid April just aren't very informative as to the eventual result. Doing the tally, for republicans, polls have a 15% relative standard error: huge when races in battleground states tend to be close to 50/50 (49/51, 48/52, 47/53, etc.)
+If we look at how [Gallup presidential election polls](https://news.gallup.com/poll/110548/gallup-presidential-election-trial-heat-trends.aspx) did between 1936 and 2008, we get a sense that polls in mid April just aren't very informative as to the eventual result. Doing the tally, for republicans, polls have a standard error of 4-5 points: huge when races in battleground states tend to be close to 50/50 (49/51, 48/52, 47/53, etc.)
 
-Moreover, these are national polls: state polls will have smaller samples and thus more uncertainty. And current pollsters are nor as good as gallup. And... there might be other sources of uncertainty that I'm missing.
+Moreover, these are national polls: polls in battleground states will have smaller samples and thus more uncertainty. And current pollsters are nor as good as gallup. And... there might be other sources of uncertainty that I'm missing. On the other hand, we have increased polarization, not all states are battleground states, and this variable seems like it requires a bit of finesse.
 
-But incorporating reasonable estimates of uncertainty, the probability of a republican win the model gives is 51%. This is now in line with [prediction markets](https://electionbettingodds.com/PresidentialParty2024.html).
+But incorporating reasonable estimates of uncertainty, the probability of a republican win the model gives is 50-60%. This does depend on how much uncertainty you inject. If you inject a lot of uncertainty, it moves closer to 50%. But on the other hand, one has to take care to not inject *too* much uncertainty, even for sure states, like, say, Alabama. This is now in line with [prediction markets](https://electionbettingodds.com/PresidentialParty2024.html).
 
 ## Notes on other models
 
@@ -162,7 +162,7 @@ It's not clear to me what I will do with this. After starting to program this, I
 
 General:
 
-- [ ] Share with Samotsvety
+- [ ] Adjust polls only for states which are legitimately uncertain, not in general
 - [ ] Think about whether I want to monetize this
   - Maybe with Vox?
   - Otherwise: add MIT license & publish
@@ -219,6 +219,7 @@ General
 - [x] Get clarity on next steps
 - [x] Make polling errors wider?
 - [x] Print more data for polls
+- [x] Share with Samotsvety
 
 ### Discarded
 

data/poll-errors/.~lock.gallup-republicans.ods#

@@ -1 +0,0 @@
-,nuno,calma,14.04.2024 19:03,file:///home/nuno/.config/libreoffice/4;

main.go

@@ -224,7 +224,7 @@ func getChanceCandidateWinsFromPollShare(candidate_p float64, poll_sample_size f
 	return getProbabilityAboveX(0.5, candidate_p, std)
 }
 
-func getChanceRepublicanWinFromPoll(poll Poll, pretty_print bool, std_additional_uncertainty float64) float64 {
+func getChanceRepublicanWinFromPoll(poll Poll, pretty_print bool) float64 {
 
 	biden_percentage, biden_exists := poll.PollResults["Biden"]
 	trump_percentage, trump_exists := poll.PollResults["Trump"]
@@ -240,8 +240,7 @@ func getChanceRepublicanWinFromPoll(poll Poll, pretty_print bool, std_additional
 	joint_trump_biden_sample_size := (biden_share + trump_share) * float64(poll.SampleSize)
 	std_error_poll_mean := math.Sqrt((normalized_trump_share * normalized_biden_share) / joint_trump_biden_sample_size)
 
-	std_error := std_error_poll_mean + std_additional_uncertainty
-	p_republican_win := getProbabilityAboveX(0.5, normalized_trump_share, std_error)
+	p_republican_win := getProbabilityAboveX(0.5, normalized_trump_share, std_error_poll_mean)
 
 	if pretty_print {
 		fmt.Printf("\n\t\tSample size: %f", joint_trump_biden_sample_size)
@@ -253,6 +252,67 @@ func getChanceRepublicanWinFromPoll(poll Poll, pretty_print bool, std_additional
 
 }
 
+func getChanceRepublicanWinFromPollPlusUncertainty(poll Poll, state State, pretty_print bool) float64 {
+
+	// Uncertainty from the state
+	n_republican_win := 0
+	for _, party := range state.PresidentialElectoralHistory {
+		if party == "R" {
+			n_republican_win++
+		}
+	}
+
+	// Get the uncertainty from the poll
+	biden_percentage, biden_exists := poll.PollResults["Biden"]
+	trump_percentage, trump_exists := poll.PollResults["Trump"]
+	if !biden_exists || !trump_exists {
+		panic("PollResults of poll filtered to have Biden/Trump doesn't have Biden/Trump")
+	}
+	biden_share := biden_percentage / 100.0 // will panic if the item is not found, but we've previously filtered for it
+	trump_share := trump_percentage / 100.0
+
+	normalized_trump_share := trump_share / (trump_share + biden_share)
+	normalized_biden_share := biden_share / (trump_share + biden_share)
+
+	joint_trump_biden_sample_size := (biden_share + trump_share) * float64(poll.SampleSize)
+	std_error_poll_mean := math.Sqrt((normalized_trump_share * normalized_biden_share) / joint_trump_biden_sample_size)
+
+	/* Inject additional uncertainty */
+	/*
+		Possible factors:
+			- National drift between now and the election (biggest one)
+			- States more uncertain than the national average
+			- Idiosyncratic factors
+			- Polls not being as good as gallup
+			- Increased polarization
+		Also note that the polls already have some error already
+	*/
+	std_additional_uncertainty := 5.0 / 100.0
+
+	if n_republican_win == 0 || n_republican_win == 6 {
+		// if solid states for the last 6 elections
+		std_additional_uncertainty = std_additional_uncertainty / 3.0
+
+		if pretty_print {
+			fmt.Printf("\n\t\tN republican wins: %d", n_republican_win)
+			fmt.Printf("\n\t\t=> Reducing additional uncertainty")
+		}
+
+	}
+
+	std_error := std_error_poll_mean + std_additional_uncertainty
+
+	// std_error := std_error_poll_mean + 0.065
+	p_republican_win := getProbabilityAboveX(0.5, normalized_trump_share, std_error)
+
+	if pretty_print {
+		fmt.Printf("\n\t\tStd with std_additional_uncertainty R: %f", 100*std_error)
+		fmt.Printf("\n\t\tPoll plus uncertainty says chance of R win: %f", p_republican_win)
+	}
+	return p_republican_win
+
+}
+
 /* Print state by state data */
 func printStates(states []State) {
 	for _, state := range states {
@@ -266,12 +326,13 @@ func printStates(states []State) {
 				p_baserate_republican_win++
 			}
 		}
-		fmt.Printf("\n\tHistorical base rate of R win: %f", p_baserate_republican_win)
+		fmt.Printf("\n\tHistorical base rate of R win: %f", p_baserate_republican_win/float64(len(state.PresidentialElectoralHistory)))
 
 		// Individual poll
 		for _, poll := range state.Polls {
 			fmt.Printf("\n\tPoll: %+v", poll)
-			_ = getChanceRepublicanWinFromPoll(poll, true, 0.0)
+			_ = getChanceRepublicanWinFromPoll(poll, true)
+			_ = getChanceRepublicanWinFromPollPlusUncertainty(poll, state, true)
 		}
 
 		// Aggregate poll
@@ -293,7 +354,8 @@ func printStates(states []State) {
 			aggregate_poll.PollResults["Trump"] = 100.0 * num_trump_votes / aggregate_sample_size
 
 			fmt.Printf("\n\tAggregate poll: %+v", aggregate_poll)
-			_ = getChanceRepublicanWinFromPoll(aggregate_poll, true, 0.0)
+			_ = getChanceRepublicanWinFromPoll(aggregate_poll, true)
+			_ = getChanceRepublicanWinFromPollPlusUncertainty(aggregate_poll, state, true)
 		}
 
 	}
@@ -364,12 +426,8 @@ func sampleFromState(state State) VotesForEachParty {
 				aggregate_poll.PollResults["Biden"] = 100.0 * num_biden_votes / aggregate_sample_size
 				aggregate_poll.PollResults["Trump"] = 100.0 * num_trump_votes / aggregate_sample_size
 
-				national_drift := 0.15
-				state_more_uncertain_than_national := 0.03
-				not_as_good_as_gallup := 0.03
-				idiosyncratic := 0.03
-				std_additional_uncertainty := national_drift + state_more_uncertain_than_national + not_as_good_as_gallup + idiosyncratic
-				p_republican_win_aggregate_polls := getChanceRepublicanWinFromPoll(aggregate_poll, false, std_additional_uncertainty)
+				p_republican_win_aggregate_polls := getChanceRepublicanWinFromPollPlusUncertainty(aggregate_poll, state, false)
+				// p_republican_win_aggregate_polls = getChanceRepublicanWinFromPoll(aggregate_poll, false)
 
 				// weight_polls := 0.75
 				// p_republican = weight_polls*p_republican_win_aggregate_polls + (1.0-weight_polls)*p_baserate_republican_win
@@ -442,7 +500,7 @@ func main() {
 		return
 	}
 
-	n_sims := 1_000_000
+	n_sims := 100_000
 
 	printStates(states)
 	fmt.Printf("\n\n")

output

@@ -0,0 +1,915 @@
+
+
+State: Colorado
+	Votes: 10
+	History: map[2000:R 2004:R 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.333333
+	Poll: {PollId:86601 SampleSize:632 PollResults:map[Biden:49 Trump:39] Date:2024-03-19 00:00:00 +0000 UTC Partisan:}
+		Sample size: 556.160000
+		Mean R: 44.318182
+		Std of mean R: 2.106434
+		Poll says chance of R win: 0.003495
+		Std with std_additional_uncertainty R: 7.106434
+		Poll plus uncertainty says chance of R win: 0.211991
+	Aggregate poll: {PollId: SampleSize:556 PollResults:map[Biden:55.68181818181817 Trump:44.31818181818181] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 556.000000
+		Mean R: 44.318182
+		Std of mean R: 2.106737
+		Poll says chance of R win: 0.003499
+		Std with std_additional_uncertainty R: 7.106737
+		Poll plus uncertainty says chance of R win: 0.212001
+
+State: Florida
+	Votes: 30
+	History: map[2000:R 2004:R 2008:D 2012:D 2016:R 2020:R]
+	Historical base rate of R win: 0.666667
+	Poll: {PollId:86529 SampleSize:875 PollResults:map[Biden:39 Kennedy:7 Stein:0 Trump:46] Date:2024-03-17 00:00:00 +0000 UTC Partisan:}
+		Sample size: 743.750000
+		Mean R: 54.117647
+		Std of mean R: 1.827169
+		Poll says chance of R win: 0.987888
+		Std with std_additional_uncertainty R: 6.827169
+		Poll plus uncertainty says chance of R win: 0.726788
+	Poll: {PollId:86634 SampleSize:1000 PollResults:map[Biden:34.6 Kennedy:6.1 Stein:1.1 Trump:49.2 West:0.5] Date:2024-04-10 00:00:00 +0000 UTC Partisan:}
+		Sample size: 838.000000
+		Mean R: 58.711217
+		Std of mean R: 1.700805
+		Poll says chance of R win: 1.000000
+		Std with std_additional_uncertainty R: 6.700805
+		Poll plus uncertainty says chance of R win: 0.903204
+	Aggregate poll: {PollId: SampleSize:1581 PollResults:map[Biden:43.4487118697645 Trump:56.5512881302355] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 1581.000000
+		Mean R: 56.551288
+		Std of mean R: 1.246648
+		Poll says chance of R win: 1.000000
+		Std with std_additional_uncertainty R: 6.246648
+		Poll plus uncertainty says chance of R win: 0.852858
+
+State: New Hampshire
+	Votes: 4
+	History: map[2000:R 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.166667
+
+State: Pennsylvania
+	Votes: 19
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:R 2020:D]
+	Historical base rate of R win: 0.166667
+	Poll: {PollId:86510 SampleSize:1132 PollResults:map[Biden:38 Kennedy:16 Trump:40 West:4] Date:2024-03-18 00:00:00 +0000 UTC Partisan:}
+		Sample size: 882.960000
+		Mean R: 51.282051
+		Std of mean R: 1.682119
+		Poll says chance of R win: 0.777019
+		Std with std_additional_uncertainty R: 6.682119
+		Poll plus uncertainty says chance of R win: 0.576075
+	Poll: {PollId:86604 SampleSize:431 PollResults:map[Biden:42 Kennedy:9 Stein:3 Trump:40] Date:2024-03-31 00:00:00 +0000 UTC Partisan:}
+		Sample size: 353.420000
+		Mean R: 48.780488
+		Std of mean R: 2.658859
+		Poll says chance of R win: 0.323239
+		Std with std_additional_uncertainty R: 7.658859
+		Poll plus uncertainty says chance of R win: 0.436744
+	Poll: {PollId:86587 SampleSize:600 PollResults:map[Biden:44 Kennedy:7 Mapstead:2 Stein:4 Trump:47 West:3] Date:2024-03-24 00:00:00 +0000 UTC Partisan:}
+		Sample size: 546.000000
+		Mean R: 51.648352
+		Std of mean R: 2.138639
+		Poll says chance of R win: 0.779572
+		Std with std_additional_uncertainty R: 7.138639
+		Poll plus uncertainty says chance of R win: 0.591306
+	Poll: {PollId:86624 SampleSize:800 PollResults:map[Biden:44 Kennedy:7 Trump:41] Date:2024-03-26 00:00:00 +0000 UTC Partisan:}
+		Sample size: 680.000000
+		Mean R: 48.235294
+		Std of mean R: 1.916218
+		Poll says chance of R win: 0.178543
+		Std with std_additional_uncertainty R: 6.916218
+		Poll plus uncertainty says chance of R win: 0.399302
+	Poll: {PollId:86533 SampleSize:775 PollResults:map[Biden:41 Kennedy:7 Stein:1 Trump:44] Date:2024-03-17 00:00:00 +0000 UTC Partisan:}
+		Sample size: 658.750000
+		Mean R: 51.764706
+		Std of mean R: 1.946879
+		Poll says chance of R win: 0.817645
+		Std with std_additional_uncertainty R: 6.946879
+		Poll plus uncertainty says chance of R win: 0.600263
+	Aggregate poll: {PollId: SampleSize:3121 PollResults:map[Biden:49.49905963545254 Trump:50.50094036454745] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 3121.000000
+		Mean R: 50.500940
+		Std of mean R: 0.894955
+		Poll says chance of R win: 0.712171
+		Std with std_additional_uncertainty R: 5.894955
+		Poll plus uncertainty says chance of R win: 0.533860
+
+State: Alabama
+	Votes: 9
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: California
+	Votes: 54
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+	Poll: {PollId:86635 SampleSize:1084 PollResults:map[Biden:54 Trump:31] Date:2024-03-25 00:00:00 +0000 UTC Partisan:}
+		Sample size: 921.400000
+		Mean R: 36.470588
+		Std of mean R: 1.585750
+		Poll says chance of R win: 0.000000
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.252417
+		Poll plus uncertainty says chance of R win: 0.000016
+	Aggregate poll: {PollId: SampleSize:921 PollResults:map[Biden:63.52941176470588 Trump:36.470588235294116] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 921.000000
+		Mean R: 36.470588
+		Std of mean R: 1.586094
+		Poll says chance of R win: 0.000000
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.252761
+		Poll plus uncertainty says chance of R win: 0.000016
+
+State: Hawaii
+	Votes: 4
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: Indiana
+	Votes: 11
+	History: map[2000:R 2004:R 2008:D 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 0.833333
+
+State: Iowa
+	Votes: 6
+	History: map[2000:D 2004:R 2008:D 2012:D 2016:R 2020:R]
+	Historical base rate of R win: 0.500000
+
+State: Massachusetts
+	Votes: 11
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+	Poll: {PollId:86630 SampleSize:1002 PollResults:map[Biden:46 Kennedy:9 Trump:28 West:1] Date:2024-03-29 00:00:00 +0000 UTC Partisan:}
+		Sample size: 741.480000
+		Mean R: 37.837838
+		Std of mean R: 1.781052
+		Poll says chance of R win: 0.000000
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.447718
+		Poll plus uncertainty says chance of R win: 0.000210
+	Aggregate poll: {PollId: SampleSize:741 PollResults:map[Biden:62.16216216216216 Trump:37.83783783783784] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 741.000000
+		Mean R: 37.837838
+		Std of mean R: 1.781628
+		Poll says chance of R win: 0.000000
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.448295
+		Poll plus uncertainty says chance of R win: 0.000210
+
+State: Ohio
+	Votes: 17
+	History: map[2000:R 2004:R 2008:D 2012:D 2016:R 2020:R]
+	Historical base rate of R win: 0.666667
+
+State: Virginia
+	Votes: 13
+	History: map[2000:R 2004:R 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.333333
+
+State: Wisconsin
+	Votes: 10
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:R 2020:D]
+	Historical base rate of R win: 0.166667
+	Poll: {PollId:86503 SampleSize:1000 PollResults:map[Biden:39.6 Kennedy:5.9 Stein:1 Trump:43.4 West:0.6] Date:2024-03-18 00:00:00 +0000 UTC Partisan:}
+		Sample size: 830.000000
+		Mean R: 52.289157
+		Std of mean R: 1.733705
+		Poll says chance of R win: 0.906647
+		Std with std_additional_uncertainty R: 6.733705
+		Poll plus uncertainty says chance of R win: 0.633055
+	Poll: {PollId:86588 SampleSize:600 PollResults:map[Biden:46 Kennedy:10 Mapstead:2 Stein:2 Trump:46 West:1] Date:2024-03-24 00:00:00 +0000 UTC Partisan:}
+		Sample size: 552.000000
+		Mean R: 50.000000
+		Std of mean R: 2.128141
+		Poll says chance of R win: 0.500000
+		Std with std_additional_uncertainty R: 7.128141
+		Poll plus uncertainty says chance of R win: 0.500000
+	Aggregate poll: {PollId: SampleSize:1382 PollResults:map[Biden:48.62518089725036 Trump:51.37481910274964] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 1382.000000
+		Mean R: 51.374819
+		Std of mean R: 1.344472
+		Poll says chance of R win: 0.846745
+		Std with std_additional_uncertainty R: 6.344472
+		Poll plus uncertainty says chance of R win: 0.585777
+
+State: Idaho
+	Votes: 4
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Kentucky
+	Votes: 8
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Louisiana
+	Votes: 8
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Mississippi
+	Votes: 6
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: New Mexico
+	Votes: 5
+	History: map[2000:D 2004:R 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.166667
+
+State: West Virginia
+	Votes: 4
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Connecticut
+	Votes: 7
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: New Jersey
+	Votes: 14
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+	Poll: {PollId:86576 SampleSize:1000 PollResults:map[Biden:41 Kennedy:7.5 Stein:0.8 Trump:35.8 West:1.2] Date:2024-03-29 00:00:00 +0000 UTC Partisan:}
+		Sample size: 768.000000
+		Mean R: 46.614583
+		Std of mean R: 1.800079
+		Poll says chance of R win: 0.030006
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.466746
+		Poll plus uncertainty says chance of R win: 0.164398
+	Aggregate poll: {PollId: SampleSize:768 PollResults:map[Biden:53.385416666666664 Trump:46.614583333333336] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 768.000000
+		Mean R: 46.614583
+		Std of mean R: 1.800079
+		Poll says chance of R win: 0.030006
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.466746
+		Poll plus uncertainty says chance of R win: 0.164398
+
+State: North Carolina
+	Votes: 16
+	History: map[2000:R 2004:R 2008:D 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 0.833333
+	Poll: {PollId:86641 SampleSize:600 PollResults:map[Biden:39 Kennedy:7.3 Trump:43.3] Date:2024-04-08 00:00:00 +0000 UTC Partisan:}
+		Sample size: 493.800000
+		Mean R: 52.612394
+		Std of mean R: 2.246989
+		Poll says chance of R win: 0.877508
+		Std with std_additional_uncertainty R: 7.246989
+		Poll plus uncertainty says chance of R win: 0.640756
+	Poll: {PollId:86640 SampleSize:1016 PollResults:map[Biden:42 Trump:45] Date:2024-03-30 00:00:00 +0000 UTC Partisan:}
+		Sample size: 883.920000
+		Mean R: 51.724138
+		Std of mean R: 1.680758
+		Poll says chance of R win: 0.847509
+		Std with std_additional_uncertainty R: 6.680758
+		Poll plus uncertainty says chance of R win: 0.601826
+	Poll: {PollId:86632 SampleSize:1401 PollResults:map[Biden:38 Kennedy:12 Stein:3 Trump:41 West:3] Date:2024-04-08 00:00:00 +0000 UTC Partisan:}
+		Sample size: 1106.790000
+		Mean R: 51.898734
+		Std of mean R: 1.501841
+		Poll says chance of R win: 0.896934
+		Std with std_additional_uncertainty R: 6.501841
+		Poll plus uncertainty says chance of R win: 0.614868
+	Poll: {PollId:86532 SampleSize:642 PollResults:map[Biden:39 Kennedy:8 Stein:1 Trump:43] Date:2024-03-17 00:00:00 +0000 UTC Partisan:}
+		Sample size: 526.440000
+		Mean R: 52.439024
+		Std of mean R: 2.176598
+		Poll says chance of R win: 0.868764
+		Std with std_additional_uncertainty R: 7.176598
+		Poll plus uncertainty says chance of R win: 0.633018
+	Poll: {PollId:86585 SampleSize:600 PollResults:map[Biden:43 Kennedy:10 Mapstead:2 Stein:3 Trump:49 West:2] Date:2024-03-24 00:00:00 +0000 UTC Partisan:}
+		Sample size: 552.000000
+		Mean R: 53.260870
+		Std of mean R: 2.123611
+		Poll says chance of R win: 0.937673
+		Std with std_additional_uncertainty R: 7.123611
+		Poll plus uncertainty says chance of R win: 0.676436
+	Aggregate poll: {PollId: SampleSize:3562 PollResults:map[Biden:47.75480991874711 Trump:52.245190081252886] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 3562.000000
+		Mean R: 52.245190
+		Std of mean R: 0.836922
+		Poll says chance of R win: 0.996348
+		Std with std_additional_uncertainty R: 5.836922
+		Poll plus uncertainty says chance of R win: 0.649753
+
+State: Utah
+	Votes: 6
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Oregon
+	Votes: 8
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: Alaska
+	Votes: 3
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Delaware
+	Votes: 3
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: Michigan
+	Votes: 15
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:R 2020:D]
+	Historical base rate of R win: 0.166667
+	Poll: {PollId:86502 SampleSize:1000 PollResults:map[Biden:40.6 Kennedy:4.6 Stein:1 Trump:44.6 West:0.6 Whitmer:49.5] Date:2024-03-18 00:00:00 +0000 UTC Partisan:}
+		Sample size: 852.000000
+		Mean R: 52.347418
+		Std of mean R: 1.711083
+		Poll says chance of R win: 0.914951
+		Std with std_additional_uncertainty R: 6.711083
+		Poll plus uncertainty says chance of R win: 0.636749
+	Poll: {PollId:86584 SampleSize:600 PollResults:map[Biden:45 Kennedy:12 Mapstead:2 Stein:3 Trump:48 West:2] Date:2024-03-24 00:00:00 +0000 UTC Partisan:}
+		Sample size: 558.000000
+		Mean R: 51.612903
+		Std of mean R: 2.115567
+		Poll says chance of R win: 0.777089
+		Std with std_additional_uncertainty R: 7.115567
+		Poll plus uncertainty says chance of R win: 0.589661
+	Poll: {PollId:86509 SampleSize:1097 PollResults:map[Biden:34 Kennedy:18 Trump:40 West:4] Date:2024-03-18 00:00:00 +0000 UTC Partisan:}
+		Sample size: 811.780000
+		Mean R: 54.054054
+		Std of mean R: 1.749116
+		Poll says chance of R win: 0.989769
+		Std with std_additional_uncertainty R: 6.749116
+		Poll plus uncertainty says chance of R win: 0.725973
+	Poll: {PollId:86531 SampleSize:616 PollResults:map[Biden:39 Kennedy:6 Stein:0 Trump:41] Date:2024-03-17 00:00:00 +0000 UTC Partisan:}
+		Sample size: 492.800000
+		Mean R: 51.250000
+		Std of mean R: 2.251640
+		Poll says chance of R win: 0.710604
+		Std with std_additional_uncertainty R: 7.251640
+		Poll plus uncertainty says chance of R win: 0.568429
+	Poll: {PollId:86603 SampleSize:709 PollResults:map[Biden:39.8 Kennedy:8.8 Trump:43] Date:2024-03-28 00:00:00 +0000 UTC Partisan:}
+		Sample size: 587.052000
+		Mean R: 51.932367
+		Std of mean R: 2.062088
+		Poll says chance of R win: 0.825645
+		Std with std_additional_uncertainty R: 7.062088
+		Poll plus uncertainty says chance of R win: 0.607814
+	Aggregate poll: {PollId: SampleSize:3301 PollResults:map[Biden:47.59470467938281 Trump:52.4052953206172] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 3301.000000
+		Mean R: 52.405295
+		Std of mean R: 0.869249
+		Poll says chance of R win: 0.997172
+		Std with std_additional_uncertainty R: 5.869249
+		Poll plus uncertainty says chance of R win: 0.659028
+
+State: Minnesota
+	Votes: 10
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+	Poll: {PollId:86625 SampleSize:608 PollResults:map[Biden:44 Trump:42] Date:2024-04-07 00:00:00 +0000 UTC Partisan:}
+		Sample size: 522.880000
+		Mean R: 48.837209
+		Std of mean R: 2.186007
+		Poll says chance of R win: 0.297389
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.852674
+		Poll plus uncertainty says chance of R win: 0.381397
+	Aggregate poll: {PollId: SampleSize:522 PollResults:map[Biden:51.16279069767442 Trump:48.83720930232558] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 522.000000
+		Mean R: 48.837209
+		Std of mean R: 2.187849
+		Poll says chance of R win: 0.297544
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.854515
+		Poll plus uncertainty says chance of R win: 0.381452
+
+State: Missouri
+	Votes: 10
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: New York
+	Votes: 28
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: North Dakota
+	Votes: 3
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Rhode Island
+	Votes: 4
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: Washington
+	Votes: 12
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+	Poll: {PollId:86605 SampleSize:600 PollResults:map[Biden:48 Trump:37] Date:2024-03-21 00:00:00 +0000 UTC Partisan:REP}
+		Sample size: 510.000000
+		Mean R: 43.529412
+		Std of mean R: 2.195419
+		Poll says chance of R win: 0.001603
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.862086
+		Poll plus uncertainty says chance of R win: 0.046927
+	Aggregate poll: {PollId: SampleSize:510 PollResults:map[Biden:56.470588235294116 Trump:43.529411764705884] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 510.000000
+		Mean R: 43.529412
+		Std of mean R: 2.195419
+		Poll says chance of R win: 0.001603
+		N republican wins: 0
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.862086
+		Poll plus uncertainty says chance of R win: 0.046927
+
+State: Georgia
+	Votes: 16
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:D]
+	Historical base rate of R win: 0.833333
+	Poll: {PollId:86530 SampleSize:760 PollResults:map[Biden:41 Kennedy:6 Stein:0 Trump:44] Date:2024-03-17 00:00:00 +0000 UTC Partisan:}
+		Sample size: 646.000000
+		Mean R: 51.764706
+		Std of mean R: 1.965998
+		Poll says chance of R win: 0.815304
+		Std with std_additional_uncertainty R: 6.965998
+		Poll plus uncertainty says chance of R win: 0.599994
+	Poll: {PollId:86583 SampleSize:600 PollResults:map[Biden:43 Kennedy:8 Mapstead:4 Stein:2 Trump:44 West:2] Date:2024-03-24 00:00:00 +0000 UTC Partisan:}
+		Sample size: 522.000000
+		Mean R: 50.574713
+		Std of mean R: 2.188296
+		Poll says chance of R win: 0.603582
+		Std with std_additional_uncertainty R: 7.188296
+		Poll plus uncertainty says chance of R win: 0.531862
+	Aggregate poll: {PollId: SampleSize:1168 PollResults:map[Biden:48.767123287671225 Trump:51.23287671232877] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 1168.000000
+		Mean R: 51.232877
+		Std of mean R: 1.462570
+		Poll says chance of R win: 0.800373
+		Std with std_additional_uncertainty R: 6.462570
+		Poll plus uncertainty says chance of R win: 0.575648
+
+State: Oklahoma
+	Votes: 7
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: South Carolina
+	Votes: 9
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: South Dakota
+	Votes: 3
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Wyoming
+	Votes: 3
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Arizona
+	Votes: 11
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:D]
+	Historical base rate of R win: 0.833333
+	Poll: {PollId:86528 SampleSize:516 PollResults:map[Biden:41 Kennedy:7 Stein:0 Trump:44] Date:2024-03-17 00:00:00 +0000 UTC Partisan:}
+		Sample size: 438.600000
+		Mean R: 51.764706
+		Std of mean R: 2.385970
+		Poll says chance of R win: 0.770234
+		Std with std_additional_uncertainty R: 7.385970
+		Poll plus uncertainty says chance of R win: 0.594419
+	Poll: {PollId:86492 SampleSize:600 PollResults:map[Biden:33 Kennedy:18 Trump:37 West:2] Date:2024-03-17 00:00:00 +0000 UTC Partisan:REP}
+		Sample size: 420.000000
+		Mean R: 52.857143
+		Std of mean R: 2.435764
+		Poll says chance of R win: 0.879601
+		Std with std_additional_uncertainty R: 7.435764
+		Poll plus uncertainty says chance of R win: 0.649601
+	Poll: {PollId:86577 SampleSize:503 PollResults:map[Biden:36 Trump:39] Date:2024-03-31 00:00:00 +0000 UTC Partisan:}
+		Sample size: 377.250000
+		Mean R: 52.000000
+		Std of mean R: 2.572217
+		Poll says chance of R win: 0.781580
+		Std with std_additional_uncertainty R: 7.572217
+		Poll plus uncertainty says chance of R win: 0.604158
+	Poll: {PollId:86582 SampleSize:600 PollResults:map[Biden:42 Kennedy:11 Mapstead:3 Stein:5 Trump:47 West:2] Date:2024-03-24 00:00:00 +0000 UTC Partisan:}
+		Sample size: 534.000000
+		Mean R: 52.808989
+		Std of mean R: 2.160294
+		Poll says chance of R win: 0.903248
+		Std with std_additional_uncertainty R: 7.160294
+		Poll plus uncertainty says chance of R win: 0.652582
+	Aggregate poll: {PollId: SampleSize:1769 PollResults:map[Biden:47.610814475803025 Trump:52.38918552419697] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 1769.000000
+		Mean R: 52.389186
+		Std of mean R: 1.187435
+		Poll says chance of R win: 0.977893
+		Std with std_additional_uncertainty R: 6.187435
+		Poll plus uncertainty says chance of R win: 0.650302
+
+State: Arkansas
+	Votes: 6
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Kansas
+	Votes: 6
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Maryland
+	Votes: 10
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: Nebraska
+	Votes: 5
+	History: map[2000:R 2004:R 2008:Split 2012:R 2016:Split 2020:Split]
+	Historical base rate of R win: 0.500000
+
+State: Nevada
+	Votes: 6
+	History: map[2000:R 2004:R 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.333333
+	Poll: {PollId:86586 SampleSize:600 PollResults:map[Biden:44 Kennedy:15 Mapstead:3 Stein:5 Trump:48 West:2] Date:2024-03-24 00:00:00 +0000 UTC Partisan:}
+		Sample size: 552.000000
+		Mean R: 52.173913
+		Std of mean R: 2.126129
+		Poll says chance of R win: 0.846722
+		Std with std_additional_uncertainty R: 7.126129
+		Poll plus uncertainty says chance of R win: 0.619841
+	Aggregate poll: {PollId: SampleSize:552 PollResults:map[Biden:47.82608695652174 Trump:52.17391304347826] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 552.000000
+		Mean R: 52.173913
+		Std of mean R: 2.126129
+		Poll says chance of R win: 0.846722
+		Std with std_additional_uncertainty R: 7.126129
+		Poll plus uncertainty says chance of R win: 0.619841
+
+State: Tennessee
+	Votes: 11
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+	Poll: {PollId:86629 SampleSize:974 PollResults:map[Biden:25 Kennedy:16 Trump:48] Date:2024-04-02 00:00:00 +0000 UTC Partisan:}
+		Sample size: 711.020000
+		Mean R: 65.753425
+		Std of mean R: 1.779618
+		Poll says chance of R win: 1.000000
+		N republican wins: 6
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.446285
+		Poll plus uncertainty says chance of R win: 0.999998
+	Aggregate poll: {PollId: SampleSize:711 PollResults:map[Biden:34.24657534246575 Trump:65.75342465753425] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 711.000000
+		Mean R: 65.753425
+		Std of mean R: 1.779643
+		Poll says chance of R win: 1.000000
+		N republican wins: 6
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.446310
+		Poll plus uncertainty says chance of R win: 0.999998
+
+State: District of Columbia
+	Votes: 3
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: Illinois
+	Votes: 19
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+State: Maine
+	Votes: 4
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:Split 2020:Split]
+	Historical base rate of R win: 0.000000
+
+State: Montana
+	Votes: 4
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+
+State: Texas
+	Votes: 40
+	History: map[2000:R 2004:R 2008:R 2012:R 2016:R 2020:R]
+	Historical base rate of R win: 1.000000
+	Poll: {PollId:86544 SampleSize:1117 PollResults:map[Biden:36 Kennedy:15 Trump:48] Date:2024-03-21 00:00:00 +0000 UTC Partisan:}
+		Sample size: 938.280000
+		Mean R: 57.142857
+		Std of mean R: 1.615572
+		Poll says chance of R win: 0.999995
+		N republican wins: 6
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.282239
+		Poll plus uncertainty says chance of R win: 0.985230
+	Poll: {PollId:86643 SampleSize:1000 PollResults:map[Biden:42.2 Kennedy:7.6 Stein:1.7 Trump:50.7 West:1] Date:2024-04-06 00:00:00 +0000 UTC Partisan:}
+		Sample size: 929.000000
+		Mean R: 54.574812
+		Std of mean R: 1.633566
+		Poll says chance of R win: 0.997449
+		N republican wins: 6
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 3.300232
+		Poll plus uncertainty says chance of R win: 0.917158
+	Aggregate poll: {PollId: SampleSize:1867 PollResults:map[Biden:44.134784285163455 Trump:55.865215714836545] Date:0001-01-01 00:00:00 +0000 UTC Partisan:}
+		Sample size: 1867.000000
+		Mean R: 55.865216
+		Std of mean R: 1.149183
+		Poll says chance of R win: 1.000000
+		N republican wins: 6
+		=> Reducing additional uncertainty
+		Std with std_additional_uncertainty R: 2.815849
+		Poll plus uncertainty says chance of R win: 0.981371
+
+State: Vermont
+	Votes: 3
+	History: map[2000:D 2004:D 2008:D 2012:D 2016:D 2020:D]
+	Historical base rate of R win: 0.000000
+
+[ 131,  132):  0.00% (0%)
+[ 132,  133):  0.00% (0%)
+[ 133,  134):  0.00% (0%)
+[ 134,  135):  0.00% (0%)
+[ 135,  136):  0.00% (0%)
+[ 136,  137):  0.00% (0%)
+[ 137,  138):  0.00% (0%)
+[ 138,  139):  0.00% (0%)
+[ 139,  140):  0.00% (0%)
+[ 140,  141):  0.00% (0%)
+[ 141,  142):  0.00% (0%)
+[ 142,  143):  0.00% (0%)
+[ 143,  144):  0.00% (0%)
+[ 144,  145):  0.00% (0%)
+[ 145,  146):  0.00% (0%)
+[ 146,  147):  0.00% (0%)
+[ 147,  148):  0.00% (0%)
+[ 148,  149):  0.00% (0%)
+[ 149,  150):  0.00% (0%)
+[ 150,  151):  0.00% (0%)
+[ 151,  152):  0.00% (0%)
+[ 152,  153):  0.00% (0%)
+[ 153,  154):  0.00% (0%)
+[ 154,  155):  0.00% (0%)
+[ 155,  156):  0.00% (0%)
+[ 156,  157):  0.00% (0%)
+[ 157,  158):  0.00% (0%)
+[ 158,  159):  0.00% (0%)
+[ 159,  160):  0.00% (0%)
+[ 160,  161):  0.00% (0%)
+[ 161,  162):  0.00% (0%)
+[ 162,  163):  0.00% (0%)
+[ 163,  164):  0.00% (0%)
+[ 164,  165):  0.00% (0%)
+[ 165,  166):  0.00% (0%)
+[ 166,  167):  0.00% (0%)
+[ 167,  168):  0.00% (0%)
+[ 168,  169):  0.00% (0%)
+[ 169,  170):  0.00% (0%)
+[ 170,  171):  0.00% (0%)
+[ 171,  172):  0.01% (0%)
+[ 172,  173):  0.00% (0%)
+[ 173,  174):  0.00% (0%)
+[ 174,  175):  0.00% (0%)
+[ 175,  176):  0.00% (0%)
+[ 176,  177):  0.00% (0%)
+[ 177,  178):  0.01% (0%)
+[ 178,  179):  0.00% (0%)
+[ 179,  180):  0.00% (0%)
+[ 180,  181):  0.00% (0%)
+[ 181,  182):  0.01% (0%)
+[ 182,  183):  0.02% (0%)
+[ 183,  184):  0.01% (0%)
+[ 184,  185):  0.01% (0%)
+[ 185,  186):  0.00% (0%)
+[ 186,  187):  0.01% (0%)
+[ 187,  188):  0.01% (0%)
+[ 188,  189):  0.02% (0%)
+[ 189,  190):  0.02% (0%)
+[ 190,  191):  0.02% (0%)
+[ 191,  192):  0.01% (0%)
+[ 192,  193):  0.02% (0%)
+[ 193,  194): █ 0.03% (0%)
+[ 194,  195):  0.01% (0%)
+[ 195,  196):  0.02% (0%)
+[ 196,  197): █ 0.03% (0%)
+[ 197,  198): █ 0.04% (0%)
+[ 198,  199): █ 0.03% (0%)
+[ 199,  200): ██ 0.05% (0%)
+[ 200,  201): █ 0.03% (0%)
+[ 201,  202): ██ 0.05% (0%)
+[ 202,  203): ██ 0.04% (1%)
+[ 203,  204): ███ 0.07% (1%)
+[ 204,  205): ██ 0.05% (1%)
+[ 205,  206): ██ 0.06% (1%)
+[ 206,  207): ███ 0.07% (1%)
+[ 207,  208): ███ 0.07% (1%)
+[ 208,  209): ████ 0.10% (1%)
+[ 209,  210): ████ 0.10% (1%)
+[ 210,  211): ████ 0.09% (1%)
+[ 211,  212): ████ 0.10% (1%)
+[ 212,  213): █████ 0.11% (1%)
+[ 213,  214): █████ 0.12% (1%)
+[ 214,  215): ██████ 0.14% (2%)
+[ 215,  216): █████ 0.12% (2%)
+[ 216,  217): ██████ 0.14% (2%)
+[ 217,  218): ██████ 0.15% (2%)
+[ 218,  219): ████████ 0.19% (2%)
+[ 219,  220): ████████ 0.18% (2%)
+[ 220,  221): █████████ 0.20% (3%)
+[ 221,  222): ████████ 0.18% (3%)
+[ 222,  223): █████████ 0.21% (3%)
+[ 223,  224): ██████████ 0.24% (3%)
+[ 224,  225): ███████████ 0.26% (3%)
+[ 225,  226): ███████████ 0.25% (4%)
+[ 226,  227): ███████████ 0.26% (4%)
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