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大選在即,兩位候選人民調(diào)結(jié)果越來越接近

SHAWN TULLY
2020-11-03

美國總統(tǒng)大選將變得異常激烈,在選舉夜之前將難分勝負(fù)。

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不要低估特朗普。特朗普在搞砸了第一次辯論并感染新冠肺炎之后,他的勝選概率大降,但之后有大幅提高。這種上升的勢頭仍在繼續(xù),如果他的支持率繼續(xù)按照這樣的速度上升,美國總統(tǒng)大選將變得異常激烈,在選舉夜之前將難分勝負(fù)。

這是西北大學(xué)(Northwestern University)數(shù)據(jù)科學(xué)家托馬斯?米勒的研究結(jié)果。米勒創(chuàng)建了一種新方法,專門用于預(yù)測今年總統(tǒng)大選的結(jié)果。米勒告訴《財(cái)富》雜志:“特朗普重新開始他所擅長的造勢活動(dòng)之后,聲望有所上升。本次大選的競爭異常激烈,雙方的差距很小,但這并沒有引起媒體的關(guān)注。你依舊會(huì)聽到許多電視節(jié)目里大談特談拜登的壓倒性優(yōu)勢,說他拿下了德克薩斯州。這是不可能的?!?/p>

米勒是西北大學(xué)數(shù)據(jù)科學(xué)項(xiàng)目的負(fù)責(zé)人。他曾經(jīng)創(chuàng)建過一個(gè)類似的計(jì)算機(jī)模型,通過模擬擊球手和投手之間的不同配對,預(yù)測職業(yè)棒球比賽的結(jié)果。他說該模型會(huì)模擬每一位球員的上場擊球次數(shù)。“我會(huì)在正式比賽之前模擬整場比賽,看看誰能獲勝,通過這種方式來確定賠率。然后我將這些賠率與博彩網(wǎng)站上的賠率相匹配,如果兩個(gè)賠率的偏差很大,就是下注的時(shí)候。我發(fā)現(xiàn)在15場比賽中,可能有一兩場值得下注?!?/p>

他在8月開始研究大選數(shù)據(jù)。但他并沒有使用民意調(diào)查數(shù)據(jù),或者經(jīng)濟(jì)狀況對大選結(jié)果的影響等歷史指標(biāo),盡管這是最常用的兩種預(yù)測大選結(jié)果的工具。他的預(yù)測基于美國知名度最高的政治博彩網(wǎng)站PredictIt上發(fā)布的賠率。米勒認(rèn)為,用政治賭客對候選人設(shè)定的“價(jià)格”作為指導(dǎo),比受訪者在接受民意調(diào)查機(jī)構(gòu)的電話調(diào)查時(shí)所說的偏好更可靠。

米勒說:“投注市場提供的賠率最為可靠,因?yàn)楫?dāng)人們在某件事上投入真金白銀的時(shí)候,你可以確信他們對這件事很有信心。如果網(wǎng)站上對特朗普的投注價(jià)格是40美分,拜登是60美分,而且你認(rèn)為拜登勝選的概率超過0.6,你就會(huì)押注拜登。這是高效政治博彩市場的魅力所在。”米勒認(rèn)為,政治期貨網(wǎng)站能夠最準(zhǔn)確地預(yù)測“群體的智慧”。

他表示,民意調(diào)查問選民會(huì)把選票投給誰,其實(shí)是在問他們希望誰贏,“而PredictIt問的是:‘你相信誰會(huì)贏?’這個(gè)問題更一針見血?!彼a(bǔ)充說,民意調(diào)查結(jié)果體現(xiàn)了幾天前收集的意見,但沒有體現(xiàn)候選人昨天的丑態(tài),或者因?yàn)楹蜻x人在辯論中表現(xiàn)出色或糟糕所帶來的支持率的巨大變化。他說:“我的預(yù)測結(jié)果比民意調(diào)查結(jié)果提前五天。我提前五天就知道第一次總統(tǒng)大選辯論的獲勝者會(huì)是拜登?!泵褚庹{(diào)查結(jié)果發(fā)布的時(shí)候就已經(jīng)過時(shí)。

米勒之所以信任PredictIt的賠率,是因?yàn)樵摼W(wǎng)站對56個(gè)司法轄區(qū)的選舉團(tuán)票分別投注,包括48個(gè)“贏者通吃”的州、內(nèi)布拉斯加州和緬因州的7個(gè)選區(qū)以及哥倫比亞特區(qū)。因此,他可以采用56個(gè)獨(dú)立政治市場中每分鐘的實(shí)時(shí)數(shù)據(jù)進(jìn)行預(yù)測。他表示,PredictIt平臺(tái)的流動(dòng)性很高,因?yàn)樵撈脚_(tái)上有10萬賭客,而且僅限于美國居民。這些人大都非常了解各縣和各州本地基層的趨勢導(dǎo)向。

他將這種方法命名為“Virtual Tout”,并在其網(wǎng)站上每小時(shí)更新一次預(yù)測結(jié)果。(或者通過推特賬號(hào)@virtualtout發(fā)布。)米勒從PredictIt平臺(tái)上提取各州市場不斷變化的賠率,并把它們匯總成兩個(gè)主要數(shù)據(jù)點(diǎn):模型預(yù)測前副總統(tǒng)拜登將贏得的選舉團(tuán)票數(shù),以及用百分比表示的拜登的勝選概率。米勒的網(wǎng)站上的一個(gè)曲線圖代表了選舉團(tuán)票的趨勢。經(jīng)過米勒的方法篩選后,當(dāng)PredictIt平臺(tái)上各州投注窗口中的賠率更支持拜登時(shí),曲線會(huì)上升。如果特朗普在56個(gè)地區(qū)的聲望升高,就像現(xiàn)在一樣,曲線就會(huì)下降。

圖中還顯示了導(dǎo)致選舉團(tuán)票數(shù)和勝選概率突然波動(dòng)的重要事件。特朗普在《60分鐘》(60 Minutes)節(jié)目中大發(fā)脾氣或米歇爾?奧巴馬在一條視頻中發(fā)表了一通肺腑之言之后,這種方法在不到一個(gè)小時(shí)內(nèi)顯示,拜登的聲望大幅提升。米勒說:“有時(shí)候我沒有看新聞,但我發(fā)現(xiàn)時(shí)間序列出現(xiàn)大幅波動(dòng),然后我才會(huì)去看新聞,了解發(fā)生了什么?!?/p>

下面讓我們回顧一下米勒的模型中,在第一階段幫助拜登聲望大漲的那些事件。米勒在8月初建立網(wǎng)站,并發(fā)現(xiàn)在整個(gè)8月份,圍繞雙方的競選活動(dòng),拜登一直以80%至85%的勝選概率領(lǐng)先于特朗普(20%至15%)。到9月初,拜登依舊領(lǐng)先,模型預(yù)測他將獲得約310張選舉團(tuán)票,但他要獲勝還需要40張選票。從9月29日的第一次辯論開始,特朗普總統(tǒng)的選情變得更糟糕。米勒說:“特朗普搞砸了第一次辯論。一周后,他被確診感染新冠病毒。我看到在消息公布之后一個(gè)小時(shí)內(nèi),拜登的選舉團(tuán)票數(shù)增加了四張。”這件事提醒美國人還有一場疫情正在威脅他們自身的健康和美國的經(jīng)濟(jì)。10月6日,特朗普神情憔悴地在沃爾特里德醫(yī)院(Walter Reed)接受治療,這時(shí)該模型預(yù)測拜登的選舉團(tuán)票達(dá)到326張,入主白宮的概率提高到94%。拜登似乎正在形成壓倒性優(yōu)勢。

然后,情況發(fā)生了變化。在10月7日副總統(tǒng)辯論的當(dāng)天,特朗普的勢頭開始反彈。但四天之后,《周六夜現(xiàn)場》(Saturday Night Live)的一段惡搞,讓特朗普的上升勢頭戛然而止。這段喜劇節(jié)目也顯示出米勒的模型對于選民情緒的快速變化極其敏感。這段節(jié)目惡搞了副總統(tǒng)辯論和落在彭斯頭上的那只網(wǎng)紅蒼蠅,而正在與妻子吉爾觀看這場辯論的拜登跳進(jìn)了時(shí)間機(jī)器,變成了那只煩人的蒼蠅,讓人回想起電影《變蠅人》(The Fly)里變形的場面。米勒說:“從午夜左右到凌晨5點(diǎn),拜登增加了多張選舉團(tuán)票。這肯定是因?yàn)椤吨芰宫F(xiàn)場》里的惡搞。有六百萬人在YouTube上觀看了這段節(jié)目。有什么更能在半夜影響人們的情緒?”

蒼蠅話題的影響沒有持續(xù)太久。10月12日,特朗普重新開始巡回造勢,在佛羅里達(dá)州斯坦福舉辦了一次聲勢浩大的集會(huì)。米勒說:“拜登的選情從此時(shí)開始進(jìn)入了下行趨勢。特朗普在奮起直追。他已經(jīng)康復(fù),從臉色和表現(xiàn)上看,他都如同獲得重生一般。” 10月5日,兩位候選人通過市政廳活動(dòng)的隔空交鋒,讓拜登的聲望有短暫攀升,但這種勢頭并未持續(xù)太久。米勒說:“兩位候選人在第二次大選辯論中的表現(xiàn)被認(rèn)為難分勝負(fù),但特朗普上升的勢頭不減?!焙髞?,特朗普在《60分鐘》節(jié)目中接受萊斯利?斯塔爾采訪時(shí)的糟糕表現(xiàn),讓他的聲望嚴(yán)重受挫。米勒說:“女性觀眾認(rèn)為他在羞辱一位備受尊敬的女性記者。他的表現(xiàn)就像是在說:‘我不在乎你,你是女人?!卑莸窃黾恿?張選舉團(tuán)票,這種上升勢頭維持了兩天。然后,特朗普止住了斯塔爾事件之后的頹勢,聲望又開始回升。

米勒說,在特朗普的聲望恢復(fù)上升時(shí),他就預(yù)測這種勢頭難以長久,而且他認(rèn)為拜登的勝選概率將重新恢復(fù)到8月至9月的水平,達(dá)到80%以上,他將獲得超過310張選舉團(tuán)票。10月28日,特朗普的勝選概率有所提升,拜登的勝選概率則下降到76.4%,選舉團(tuán)票為242張。到次日下午三點(diǎn)左右,拜登的勝選概率小幅提升到78.7%。米勒依舊認(rèn)為,拜登的領(lǐng)先幅度將從幾周前的4比1縮小到3比1。他說:“我承認(rèn)民主黨領(lǐng)先,但共和黨也在努力追趕,而且這絕不是壓倒性優(yōu)勢。特朗普絕對有勝選的可能,所有人都應(yīng)該知道這一點(diǎn)?!保ㄘ?cái)富中文網(wǎng))

翻譯:劉進(jìn)龍

審校:汪皓

不要低估特朗普。特朗普在搞砸了第一次辯論并感染新冠肺炎之后,他的勝選概率大降,但之后有大幅提高。這種上升的勢頭仍在繼續(xù),如果他的支持率繼續(xù)按照這樣的速度上升,美國總統(tǒng)大選將變得異常激烈,在選舉夜之前將難分勝負(fù)。

這是西北大學(xué)(Northwestern University)數(shù)據(jù)科學(xué)家托馬斯?米勒的研究結(jié)果。米勒創(chuàng)建了一種新方法,專門用于預(yù)測今年總統(tǒng)大選的結(jié)果。米勒告訴《財(cái)富》雜志:“特朗普重新開始他所擅長的造勢活動(dòng)之后,聲望有所上升。本次大選的競爭異常激烈,雙方的差距很小,但這并沒有引起媒體的關(guān)注。你依舊會(huì)聽到許多電視節(jié)目里大談特談拜登的壓倒性優(yōu)勢,說他拿下了德克薩斯州。這是不可能的?!?/p>

米勒是西北大學(xué)數(shù)據(jù)科學(xué)項(xiàng)目的負(fù)責(zé)人。他曾經(jīng)創(chuàng)建過一個(gè)類似的計(jì)算機(jī)模型,通過模擬擊球手和投手之間的不同配對,預(yù)測職業(yè)棒球比賽的結(jié)果。他說該模型會(huì)模擬每一位球員的上場擊球次數(shù)。“我會(huì)在正式比賽之前模擬整場比賽,看看誰能獲勝,通過這種方式來確定賠率。然后我將這些賠率與博彩網(wǎng)站上的賠率相匹配,如果兩個(gè)賠率的偏差很大,就是下注的時(shí)候。我發(fā)現(xiàn)在15場比賽中,可能有一兩場值得下注?!?/p>

他在8月開始研究大選數(shù)據(jù)。但他并沒有使用民意調(diào)查數(shù)據(jù),或者經(jīng)濟(jì)狀況對大選結(jié)果的影響等歷史指標(biāo),盡管這是最常用的兩種預(yù)測大選結(jié)果的工具。他的預(yù)測基于美國知名度最高的政治博彩網(wǎng)站PredictIt上發(fā)布的賠率。米勒認(rèn)為,用政治賭客對候選人設(shè)定的“價(jià)格”作為指導(dǎo),比受訪者在接受民意調(diào)查機(jī)構(gòu)的電話調(diào)查時(shí)所說的偏好更可靠。

米勒說:“投注市場提供的賠率最為可靠,因?yàn)楫?dāng)人們在某件事上投入真金白銀的時(shí)候,你可以確信他們對這件事很有信心。如果網(wǎng)站上對特朗普的投注價(jià)格是40美分,拜登是60美分,而且你認(rèn)為拜登勝選的概率超過0.6,你就會(huì)押注拜登。這是高效政治博彩市場的魅力所在?!泵桌照J(rèn)為,政治期貨網(wǎng)站能夠最準(zhǔn)確地預(yù)測“群體的智慧”。

他表示,民意調(diào)查問選民會(huì)把選票投給誰,其實(shí)是在問他們希望誰贏,“而PredictIt問的是:‘你相信誰會(huì)贏?’這個(gè)問題更一針見血。”他補(bǔ)充說,民意調(diào)查結(jié)果體現(xiàn)了幾天前收集的意見,但沒有體現(xiàn)候選人昨天的丑態(tài),或者因?yàn)楹蜻x人在辯論中表現(xiàn)出色或糟糕所帶來的支持率的巨大變化。他說:“我的預(yù)測結(jié)果比民意調(diào)查結(jié)果提前五天。我提前五天就知道第一次總統(tǒng)大選辯論的獲勝者會(huì)是拜登?!泵褚庹{(diào)查結(jié)果發(fā)布的時(shí)候就已經(jīng)過時(shí)。

米勒之所以信任PredictIt的賠率,是因?yàn)樵摼W(wǎng)站對56個(gè)司法轄區(qū)的選舉團(tuán)票分別投注,包括48個(gè)“贏者通吃”的州、內(nèi)布拉斯加州和緬因州的7個(gè)選區(qū)以及哥倫比亞特區(qū)。因此,他可以采用56個(gè)獨(dú)立政治市場中每分鐘的實(shí)時(shí)數(shù)據(jù)進(jìn)行預(yù)測。他表示,PredictIt平臺(tái)的流動(dòng)性很高,因?yàn)樵撈脚_(tái)上有10萬賭客,而且僅限于美國居民。這些人大都非常了解各縣和各州本地基層的趨勢導(dǎo)向。

他將這種方法命名為“Virtual Tout”,并在其網(wǎng)站上每小時(shí)更新一次預(yù)測結(jié)果。(或者通過推特賬號(hào)@virtualtout發(fā)布。)米勒從PredictIt平臺(tái)上提取各州市場不斷變化的賠率,并把它們匯總成兩個(gè)主要數(shù)據(jù)點(diǎn):模型預(yù)測前副總統(tǒng)拜登將贏得的選舉團(tuán)票數(shù),以及用百分比表示的拜登的勝選概率。米勒的網(wǎng)站上的一個(gè)曲線圖代表了選舉團(tuán)票的趨勢。經(jīng)過米勒的方法篩選后,當(dāng)PredictIt平臺(tái)上各州投注窗口中的賠率更支持拜登時(shí),曲線會(huì)上升。如果特朗普在56個(gè)地區(qū)的聲望升高,就像現(xiàn)在一樣,曲線就會(huì)下降。

圖中還顯示了導(dǎo)致選舉團(tuán)票數(shù)和勝選概率突然波動(dòng)的重要事件。特朗普在《60分鐘》(60 Minutes)節(jié)目中大發(fā)脾氣或米歇爾?奧巴馬在一條視頻中發(fā)表了一通肺腑之言之后,這種方法在不到一個(gè)小時(shí)內(nèi)顯示,拜登的聲望大幅提升。米勒說:“有時(shí)候我沒有看新聞,但我發(fā)現(xiàn)時(shí)間序列出現(xiàn)大幅波動(dòng),然后我才會(huì)去看新聞,了解發(fā)生了什么?!?/p>

下面讓我們回顧一下米勒的模型中,在第一階段幫助拜登聲望大漲的那些事件。米勒在8月初建立網(wǎng)站,并發(fā)現(xiàn)在整個(gè)8月份,圍繞雙方的競選活動(dòng),拜登一直以80%至85%的勝選概率領(lǐng)先于特朗普(20%至15%)。到9月初,拜登依舊領(lǐng)先,模型預(yù)測他將獲得約310張選舉團(tuán)票,但他要獲勝還需要40張選票。從9月29日的第一次辯論開始,特朗普總統(tǒng)的選情變得更糟糕。米勒說:“特朗普搞砸了第一次辯論。一周后,他被確診感染新冠病毒。我看到在消息公布之后一個(gè)小時(shí)內(nèi),拜登的選舉團(tuán)票數(shù)增加了四張。”這件事提醒美國人還有一場疫情正在威脅他們自身的健康和美國的經(jīng)濟(jì)。10月6日,特朗普神情憔悴地在沃爾特里德醫(yī)院(Walter Reed)接受治療,這時(shí)該模型預(yù)測拜登的選舉團(tuán)票達(dá)到326張,入主白宮的概率提高到94%。拜登似乎正在形成壓倒性優(yōu)勢。

然后,情況發(fā)生了變化。在10月7日副總統(tǒng)辯論的當(dāng)天,特朗普的勢頭開始反彈。但四天之后,《周六夜現(xiàn)場》(Saturday Night Live)的一段惡搞,讓特朗普的上升勢頭戛然而止。這段喜劇節(jié)目也顯示出米勒的模型對于選民情緒的快速變化極其敏感。這段節(jié)目惡搞了副總統(tǒng)辯論和落在彭斯頭上的那只網(wǎng)紅蒼蠅,而正在與妻子吉爾觀看這場辯論的拜登跳進(jìn)了時(shí)間機(jī)器,變成了那只煩人的蒼蠅,讓人回想起電影《變蠅人》(The Fly)里變形的場面。米勒說:“從午夜左右到凌晨5點(diǎn),拜登增加了多張選舉團(tuán)票。這肯定是因?yàn)椤吨芰宫F(xiàn)場》里的惡搞。有六百萬人在YouTube上觀看了這段節(jié)目。有什么更能在半夜影響人們的情緒?”

蒼蠅話題的影響沒有持續(xù)太久。10月12日,特朗普重新開始巡回造勢,在佛羅里達(dá)州斯坦福舉辦了一次聲勢浩大的集會(huì)。米勒說:“拜登的選情從此時(shí)開始進(jìn)入了下行趨勢。特朗普在奮起直追。他已經(jīng)康復(fù),從臉色和表現(xiàn)上看,他都如同獲得重生一般?!?10月5日,兩位候選人通過市政廳活動(dòng)的隔空交鋒,讓拜登的聲望有短暫攀升,但這種勢頭并未持續(xù)太久。米勒說:“兩位候選人在第二次大選辯論中的表現(xiàn)被認(rèn)為難分勝負(fù),但特朗普上升的勢頭不減。”后來,特朗普在《60分鐘》節(jié)目中接受萊斯利?斯塔爾采訪時(shí)的糟糕表現(xiàn),讓他的聲望嚴(yán)重受挫。米勒說:“女性觀眾認(rèn)為他在羞辱一位備受尊敬的女性記者。他的表現(xiàn)就像是在說:‘我不在乎你,你是女人?!卑莸窃黾恿?張選舉團(tuán)票,這種上升勢頭維持了兩天。然后,特朗普止住了斯塔爾事件之后的頹勢,聲望又開始回升。

米勒說,在特朗普的聲望恢復(fù)上升時(shí),他就預(yù)測這種勢頭難以長久,而且他認(rèn)為拜登的勝選概率將重新恢復(fù)到8月至9月的水平,達(dá)到80%以上,他將獲得超過310張選舉團(tuán)票。10月28日,特朗普的勝選概率有所提升,拜登的勝選概率則下降到76.4%,選舉團(tuán)票為242張。到次日下午三點(diǎn)左右,拜登的勝選概率小幅提升到78.7%。米勒依舊認(rèn)為,拜登的領(lǐng)先幅度將從幾周前的4比1縮小到3比1。他說:“我承認(rèn)民主黨領(lǐng)先,但共和黨也在努力追趕,而且這絕不是壓倒性優(yōu)勢。特朗普絕對有勝選的可能,所有人都應(yīng)該知道這一點(diǎn)?!保ㄘ?cái)富中文網(wǎng))

翻譯:劉進(jìn)龍

審校:汪皓

Don't count Donald Trump out. His odds have improved substantially since bottoming after he blew the first debate and contracted COVID-19. That upward momentum is still in place, and if it continues at the same pace, the race could be too close to call by election eve.

Those are the findings of Thomas Miller, a Northwestern University data scientist who created a new methodology tailored to predicting the outcome of this presidential election. "Trump's picked up since he got back on the trail doing his thing," Miller told Fortune. "This is a very competitive race that's tightening, but the media hasn't picked up on it. You still hear lots of talk on TV about a landslide, with Biden taking Texas. That's unlikely."

Miller, director of the Northwestern data science program, created similar computer models to forecast the outcome of professional baseball games based on simulating individual matchups between batters and pitchers—every single at-bat is modeled, he says. "I play every game in its entirety before it happens, see who wins, and that's how I establish the odds. Then I match those odds with those on the betting sites, and if there’s a major divergence, that's the time to bet. I found that out of 15 games, maybe one or two are worth betting on."

In August he started crunching data on the election. But instead of using the two most common tools—weighing the polling numbers or using such historical measures as how the economy is likely to shape the outcome—he based his predictions on the odds posted on America's most prominent political gaming site, PredictIt. For Miller, the "prices" that political gamblers place on the candidates are a far more reliable guide than the preferences that respondents state in pollsters’ telephone surveys.

"These betting markets provide the best odds because when people put their own money into something, you can be sure that's what they believe," says Miller. "When Trump's posted price is 40 cents and Biden's is 60 cents, and you think Biden's chances are better than 0.6, you'll bet on Biden. That's the beauty of an efficient political marketplace." For Miller, the political futures sites best project "the wisdom of the crowd."

Miller notes that the surveys ask people whom they'll vote for, meaning whom they'd like to win: “PredictIt effectively asks, ‘Whom do you believe will win?’ That's the better question." He adds that polling results reflect opinions collected days before, and not the gaffe the candidate committed yesterday, or the big shift in support in the hours after a good or bad debate. "My results are out five days before the polls come out," he adds. "I was five days in advance knowing the first presidential debate was won by Biden." By the time they appear, polling results are already out of date.

Miller relies on PredictIt because the site takes bets on 56 separate jurisdictions awarded electoral votes: the 48 "winner-take-all" states, and seven districts in Nebraska and Maine, as well as the District of Columbia. Hence, he's able to deploy real-time, minute-by-minute data from what are effectively 56 separate political markets. He notes that the PredictIt platform is highly liquid, since it boasts 100,000 bettors, and that it's restricted to U.S. residents, many of whom are knowledgeable about the on-the-ground, bellwether trends in their counties and states.

The methodology, trademarked the Virtual Tout, updates the forecasts every hour on his website. (Or at Twitter at @virtualtout.) Miller distills the shifting odds in PredictIt’s mainly state-by-state markets into two principal data points: first, the number of electoral votes that the model forecasts Biden will win, and second, the former vice president's chance of victory, shown as a percentage. Miller’s site shows a curve representing the trend in electoral votes. The curve rises when the PredictIt odds from the state betting windows, filtered through Miller's methodology, move in Biden's favor. The trajectory descends, as now, when Trump's fortunes across the 56 markets improve.

Superimposed on the graph are important events, many of which cause an immediate spike or cratering in the candidates' electoral count and odds of winning. In less than an hour, the methodology registers Biden's bump from Trump's angry outburst on 60 Minutes or Michelle Obama's heartfelt video message. "Sometimes I haven't been listening to the news, and I see the time series move dramatically, then I turn on the news to see what made it happen," says Miller.

Let's trace the events that in the first phase measured by Miller brought a big uptick in Biden's fortunes. Miller launched the site in early August and found that Biden held an edge of 80% to 85% to Trump's 20% to 15% during the entire month that encompassed both campaigns. By early September, Biden was holding that lead, and the model gave him around 310 electoral votes, 40 more than needed for victory. Starting with the first debate on Sept. 29, things got even worse for the President. "He blew the first debate," says Miller. "A week later, he's diagnosed with COVID-19. I could see Biden's count jump by four votes within an hour of the announcement." That reminded Americans of the plague threatening their health and the economy. On Oct. 6, as Trump languished in Walter Reed hospital, Biden's numbers hit their high-water mark of 326 electoral votes and a 94% probability of taking the White House. A Biden landslide appeared to be building.

Then, the momentum shifted. The start of Trump's comeback coincided with the vice presidential debate on Oct. 7. But in a comical episode that also shows the sensitivity of Miller's model to passing changes in voters' mood, Trump suffered a blip following the Saturday Night Live skit four days later. The SNL parody of the VP debate showed the famous fly sticking to Pence's head, and Biden, who had been watching the face-off with wife Jill, jumping into a time machine to be transformed into the offending insect, recalling the metamorphosis in the movie The Fly. "From around midnight to 5 a.m., Biden gained a few votes," says Miller. "It must have been the SNL skit. Six million people viewed it on YouTube. What else would move the needle in the middle of the night?"

The fly didn't sting for long. On Oct. 12, Trump returned to barnstorming, hosting a signature raucous rally in Stanford, Fla. "The downward slope for Biden began," says Miller. "Trump's back on the trail. He's recovered and acts, and looks, reborn." The dueling town halls on Oct. 5 gave Biden a brief lift that quickly faded. "The second debate was regarded as a draw, but Trump's momentum continued," says Miller. Then Trump suffered what looked like a serious setback from his obstreperous performance in his 60 Minutes interview with Lesley Stahl. "Women viewers perceived that he was insulting a respected female journalist," says Miller. "It's as if he was saying, 'I don't care about you, you're a woman.'" Biden gained around five electoral votes and benefited for two days. Then Trump's gains got right back on the track they'd jumped after the Stahl debacle.

Miller says that when the Trump resurgence started, he expected it to be short-lived and thought that Biden would resume the 80%-plus odds and over 310 electoral votes he'd enjoyed from August through September. On Oct. 28, Trump's chances improved as Biden’s slipped to 76.4% and 242 electoral votes. By mid-afternoon the next day, Biden had gained a bit to 78.7%. Miller still puts Biden's odds of victory at 3-to-1, down from 4-to-1 a few weeks ago. "I would say the Democrats have the lead, but the Republican ticket is catching up, and this is by no means a landslide," he says. "Trump can absolutely win, and everyone should be aware of that."

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