Very interesting read from Justin Wolfers at the New York Times' Freakonomics blog, who cites research from friend-of-538 Robert Erikson which suggests that polls tend to understate the performance of the incumbent. Political scientists Robert Erikson (of Columbia) and Christopher Wlezien (of Temple) have recently mined daily polling reports from the last half-century of elections, mapping the relationship between early polling numbers and final election returns. At this point in the race, they find that around half of any lead should be discounted, as early advantages tend to dissipate. (You can read the full paper here, or an ungated version here.)
I just looked at this too. Although I doubt that my methodology is anywhere near as robust, I found the same thing that Erikson did: you would need to discount a polling lead more heavily for an incumbent than for a challenger.
Profs. Erikson and Wlezien point to another reason to be wary of Sen. Obama’s early polling lead: On average, the voting public tends to be more strongly anti-incumbent three-and-a-half years into an administration than they are on Election Day. Based on patterns in previous cycles, the professors suggest that this exaggerated anti-incumbent feeling is boosting Sen. Obama’s lead by around three percentage points.
So if you first halve Obama’s six point lead, then subtract a three point anti-incumbency bias, you are left with a dead heat.
The problem is that while McCain comes from the incumbent party, McCain himself is not an incumbent. He is not even a pseudo-incumbent (a.k.a. the sitting Vice President), the first time this situation has occurred since 1952.
Things start to get fairly complicated if you look at the interaction effects between a candidate's lead in the polling, the number of days until the election, and the incumbency, especially since there are different degrees of incumbency, and also interaction effects and various other sorts of non-linearity between all these different variables.
But from what best I can tell, the incumbent effect that Wolfers and Erikson have identified is smaller when we're dealing with the incumbent party rather than an actual, incumbent President -- probably more like one point rather than three at this stage of the cycle. And in '52, when you had neither an incumbent President nor a sitting Vice President running, the large lead that Dwight Eisenhower had in the polling held up quite well.
My general philosophy behind my modeling is to make everything "candidate-neutral". The model knows that there are two candidates and that they have certain polling numbers, but it doesn't know who is a Republican or who is a Democrat, or who is an incumbent and who isn't. So I won't say "the polling numbers will move toward Candidate X", although I do say "the polling numbers are likely to move toward whichever candidate happens to be trailing".
If I did look at that stuff, the numbers might be moved a couple points in McCain's direction, because of this incumbent issue I just described and also because there has been some tendency for the polling to overstate the performance of the Democrat. On the other hand, if one starts to consider candidate-related variables, there are another whole set of 'meta' variables that one might want to evaluate too, such as the condition of the economy, the presence of a war, incumbent approval ratings, and party registration figures. Most of those factors would tend to favor Mr. Obama.
Making things candidate neutral is partially a marketing decision -- I can't imagine how much yelling and screaming there would be if I said "let's give McCain 2 bonus points because he's a Republican" or "let's give Obama 2 bonus points because the economy stinks". But also, the set of past polling data is not that robust -- about 14 elections that were polled scientifically, in only the last several of which did you have multiple agencies releasing polling data at regular intervals. If you want to look at something like "Democrat challenging Republican quasi-incumbent in wartime with crappy economy", your dataset gets down to zero pretty quickly.
7.09.2008
Quibble
by Nate Silver @ 12:42 PM...see also meta, methodology
Subscribe to:
Post Comments (Atom)

54 comments
Nate, don't know if you saw that the Rasmussen MO is out with McCain +5 (47-42 and 50-45 with leaners).
The main point is that we already know who the candidates are, and what the environment is like, for this election, so that any decision we make about how to incorporate such variables will have to be biased, consciously or not. We say "this must matter" but some part of us would go for this because IT HELPS OBAMA. We can not make this decision blindly. So indeed better avoid this NOW.
Come December, you should make a decision on how to incorporate meta variables in future elections, and use this decision from 2012 onwards (when, by the way, you will be already established as the major source for data-based political analysis).
"So if you first halve Obama’s six point lead, then subtract a three point anti-incumbency bias, you are left with a dead heat"
Intuitively, this doesn't seem correct...because, if you subtract the three points first, and THEN halve it, you end up with Obama having a 1.5 point lead. Yeah, essentially that's the same as a dead heat at this point, but still...the point is, you come up with a different result. Is there a way to incorporate both adjustmets into one? That would seem like a more correct way of doing it. I could easily be wrong, though.
" Nate, don't know if you saw that the Rasmussen MO is out with McCain +5 (47-42 and 50-45 with leaners).
"
Since he cooperates with Rasmussen, I´m sure that if he does not know the poll results before they are published, he receives their free poll update, at least. And I think every poll freak checks Rasmussen 20x a day (like I do) because they publish most polls. SUSA comes next.
The only polls which are hard to find are unknown pollster polls and university polls. Like SMOR or Texas Lyceum or Baselice or so.
Rasmussen or SUSA is easy.
"The problem is that while McCain comes from the incumbent party, McCain himself is not an incumbent. He is not even a pseudo-incumbent (a.k.a. the sitting Vice President), the first time this situation has occurred since 1952."
Even if McCain WERE a sitting vice president, I'm not sure that would be much of an advantage. The sitting VP running for president has lost four out of the last five elections.
Nate,
I would take exception with applying the "incumbent analysis" to this election. There definitely is an early fatigue against the incumbent President, which corrects as the election gets closer. There is a much different fatigue over seven years into an administration.
A better model would focus on elections following a two term (post 22nd Amendment) incumbent (1960, 1976, 1988, 2000). A universe of four is not much to work with, though we can observe that all four elections were close affairs, and the incumbent party lost three of four.
In 1960, the race was neck-and-neck from June through November. In 1976, Ford was far behind in July, but surged, and lost the popular vote narrowly. In 1988, Bush was behind until the infamous Willie Horton ads, and went on to win a narrow popular vote victory. In 2000, another Bush led most polls during the summer, and the race was neck-and-neck until Gore won the popular vote and lost the EV. A good resource is this paper, containing a graph on page 10, tracking all elections from 1952 to 1992.
Given these four elections as models, it is arguable that there was some anti-incumbent bias which rubbed off on the incumbent VP, and this bias corrected over time. Does this mean an anti-incumbent bias has rubbed off on McCain, and this will correct over time? That is an interesting question, but I believe it overlooks important exogenous factors in the current election.
This election has more than an "anti-incumbency" bias; this election appears to have an "anti-ideology" bias, representing a pendulum swing back to the center, after 26 years of moving to the right (if we assume 1980 as the start of the last swing, and 2006 as the start of the current swing). This is reflected in things such as the "enthusiasm gap" and other measures of the motivation and mood of Democrats, Republicans and independents.
Probably the best model to look at is 1980, where Reagan won a narrow race at a point I would identify as a race defined by an "anti-ideology" bias.
So will polls move back towards McCain over the course of this election? Almost certainly. However, I think to include a correction for "anti-incumbent" bias in this election in your model will cause overcorrection, since I think it is at best a very minor factor, swamped by other, more important factors.
Too much analysis, geez. I've heard so many opinions this year from pundits and historical experts, what a pile of crap. Obama should win because of the economy and the wars and people hate Bush, its that simple. Everything else is over analysis. Obama "should" win by around 4-5 points just based on atmospherics. All the math in the world can't make up for common sense.
Common sense says Obama should win. That doesen't mean he will, but everyone level headed agrees he should. Any Democrat should win this year. If Hillary was the candidate, it would be more certain. The R's would be in deep trouble. She was stronger electorally than Obama. But the Democrat should win this year regardless.
Too much analysis, geez. I've heard so many opinions this year from pundits and historical experts, what a pile of crap. Obama should win because of the economy and the wars and people hate Bush, its that simple. Everything else is over analysis.
If you feel that way, why are you even on this site?
I have a quibble Nate. Why do you have Obama's chances of winning in Mississippi at 8%. McCain is now going up with TV ads in the state! Obviously his internal polling is showing something in Mississippi that is not making him happy. I know you do not put in such things as TV ad buys or voter registration numbers in your formula, but at some point it may be necessary to take into consideration some real world factors such as what is going on on the ground in these states to create a better predicator of where those states will go.
knutsondc @11:39:
By and large I think you're right. When I thought it over, I am pretty sure that even though I can forward the e-mail I get inviting me to the Zogby poll, whomever I forwarded it to would need to "register" before they could take the poll.
I do think though that since Harris "pays" (OK at a rate that's derisory compared to what I could get doing just about anything else for pay) and Zogby doesn't, that means that people who sign up for Zogby have to be extra-interested in politics and current events, or maybe just extra-fond of taking polls, compared to the general population.
BTW I often find the Zogby questions framed in such a way that I can't answer them. They are never open-ended. The "what is the most important issue for you this election" is particularly egregious. I got out of the habit of taking them for a while -- I felt (not unreasonably!) that I was being used to support someone else's unknown agenda.
anon 12:36 -
just not true that Clinton was stronger electorally. At every point during the primary (with the exception of a couple of weeks) Obama strongly outperformed Clinton against McCain in the state polls. Look it up...I do agree that, barring some earth-shaking event, the likelihood is a 4-6 point pop vote win for Obama and somewhere from 320 to 370 EV. If it gets to 6 or 7 points, that may translate into a Reagan 1980 landslide (people tend to forget he won the pop vote by only 7 points, and Bush senior won by only 8, which translated into 400 EVs)
This discussion misses the important thing about being an incumbent (maybe even an incumbent VP) - the candidate can DO things. Sign bills, respond to disasters, that sort of stuff. That can't "rub off" on an incumbent party candidate.
Neither McCain nor Obama are "doing" much in their day jobs (they are still Senators, right?). If one of them could take decisive action in some way in their Senatorial capacity, it might help out.
I'm sure there's more to this swing-towards-the-incumbent tendency of course, but maybe not much more.
Sorry, that comment obviously belongs in the Zogby thread.
The last sentence in the column is money. This is over-analysis by Robert Erikson and a case of looking strictly at trends without trying to actually desccribe what is happeneing. In fact it seems fairly backward, a trend is noticed and then a rationalization is presented. Of course properly it should be a hypotheis is created and tested as being falsifiable. And the hypothesis is not incumbants do b etter over time, the hypothesis needs to be "Since incumbants control policy decisions and can in a sense direct public discourse in their favor, they tend to be able to improve their chances as the election approaches. If this hypothesis is true I should see it in the polling numbers." That is the broad strokes, but it seems to me to be the proper approach.
@Anonymous 12:36pm:
If we don't need numbers, then why do we even poll? Or vote, for that matter? If "everyone level headed" knows Obama should win, then why even have an election?
It's funny - people with the same "numbers are scary" attitude don't like Nate's work about baseball, either. "This team will win because they have 'proven veterans' or 'know how to win,'" etc.
If there aren't enough data points in presidential elections, what about gubernatorial races? I'm sure there must be some recent examples of a same-party candidate running to succeed an unpopular governor.
People discount Obama's organizational strength with an unprecedented 5000 local organizers, who organize local volunteers who register multiple new voters.
Days left to the general election: 117
It would be interesting to know what's the target number of new registrations are in the following states:
GA, NC, MO, ND, OH, PA, CO, VA, NM, NV, FL, MI, IN, WI, MN and OR?
That would be a good number to predict based on census data, specific demographics of potential unregistered voters in each state.
Such factors would explain why MuCain doesn't distance himself from Bush that much. Hence, the continuing need for hyper turnout motivation for Obama.
Yeah, I would much prefer that this site stay away from this sort of astrology and guesswork, like the "voters will break against the incumbent 2-1" bullshit that many people mislead themselves with in 2004. It's much like all the dumb statistics people like to throw out during sports games -- "a team with a perfect record has never gone on to win the championships!" -- which has absolutely no predictive value whatsoever. Even accounting for the results tightening as we move toward election day is something I'm not a fan of, but if there's solid, consistent scientific evidence to back it up, I guess I'll have to live with it.
-illissius
Also, Obama is actively characterizing McCain as an extension of Bush, forcing him towards actually being the incumbent. I'm also unconvinced at the assertion that Presidential approval ratings significantly rise from summer to election day. Looking at Wikipedia charts (yes, yes, I know), it did not happen significantly with Bush 43, did not happen with Bill Clinton, and I can't quite tell with HW if the approval spike was before or after the election. If anyone has better resolution data on this, I'd be happy to admit I'm wrong, tho.
Nate: The very last thing you should ever do is throw arbitrary, impossible to quantify except by "gut instinct" variables into a model. This election is in uncharted waters. There's NEVER been an election where the incumbent party President was at 28% or below and 80% of the population thinks the country is "on the wrong track."
I'm not sure why we're having a discussion of "incumbency advantage" when there's NO incumbent in this race.
John McCain is NOT an incumbent! If he wanted to run openly as a successor to Bush's policies he COULD qualify as an incumbent in a sense, but since Bush's popularity is the worst in recorded history that would be suicidal.
Instead, McCain has to spend most of his time denying that he's running for Bush's third term, all his advertising for instance talks about "he stood up to the Party on Global Warming" for instance. He's trying to distance himself from Bush as much as humanly possible, while still having an "R" next to his name. Even that is probably fatal on election day. In short, he probably can't run far enough.
Given that set of circumstances, stick to the polling numbers. If we wanted some whacky Rube-Goldberg machine type theory to predict the election result we can always go to Pollyvote.com (BTW: their current tracker as of July 9 is 47.4% for the Republican vote).
Gut instinct is a terrible way to predict anything and adding factors that have some statistical correlation, but we can't explain WHY or exactly HOW STRONGLY they are corrleated (such as economic indicators 6 months before an election) and especially since these factors are based on very FEW results (a hand-full of national elections) doesn't help.
McCain could be on-air in Miss for a variety if reasons including the senate race there, the desire to make Haley Barbour happy, the deisre to raise money from the evangelical delta circuit - there are lots of reasons beyond he might think he's behind
Anon 12:49:
The 8 percent win percentage is based on NUMBERS from the polls, not anything Nate is doing.
I heard the Mississippi ad thing was a typo from MI to MS, but not sure on that.
I see, to my surprise, that many seem to be against the inclusion of meta-variables *as a matter of principle*.
It is perhaps not clear enough that Nate engages in two separate exercises which are lumped together in his win percentage.
The first is trying to project, given the current polling, the distribution of probabilities for electoral results - had the elections took place tomorrow.
The second is trying to project, given the current polling, the distribution of probabilities for the polling on Election Day.
The 65% we get can more or less be interpreted as a multiplication of two circa 80% (somewhat more than this - for winning given the current polling; rather less than this - for maintaining the current polling or better by Election Day).
The first is very safe; the second is very problematic. For the first, polling data are essentially all we need; for the second, polling data, even when combined with the evidence of past polling, are clearly not the only useful source of information.
What I think Nate ought to do is to find the best tool for projecting the elections outcome based on meta-variables, and use this as the target towards which polling results are made to regress (right now, the target is taken automatically as 50%, which *on average should be just fine*).
But as I said above, in the second comment on this thread, he should only do this starting with 2012!
McCain's numbers may improve by November but I doubt you could attribute this to an incumbency effect, just because he's in the incumbent's party. Given the all-time low approval rating of the incumbent President, any ties to the incumbent are probably more harmful than helpful. I'm not sure we have really good historical examples of this, an incredibly unpopular term-limited President with two non-incumbents. Does the non-incumbent in the sitting President's party really get a boost in November?
Couldn't this just as easily be attributed this to name recognition or "the-devil-you-know" phenomena?
Voters make last second decisions at the polls simply to fill holes in their ballots. I'd like to see the data that suggests that this isn't what is really happening here.
Thank you, Cugel. I was beginning to wonder if I was the only person who remembered that McCain isn't the incumbent. Nate says it in his post.
(Although, I guess the Obama campaign must be getting somewhere if the brainy commenters of 538 are writing as though a McCain election would in fact be Bush's third term...)
(on a completely unrelated note, are any of you coming here to Austin next week? Would love to meet some of my new pals--plus, this is my hometown. While we have no baseball, I'm sure we can get together and obsess about the weight that just being a Yankee should be given in All-Star voting.)
Nate Silver: If you want to look at something like "Democrat challenging Republican quasi-incumbent in wartime with crappy economy", your dataset gets down to zero pretty quickly.
True.
But if you want to look at something like "Does the challenging or incumbent party do better in times of a crashing economy, quickly rising food & fuel costs, and multiple crises in the Middle East?", then the 1976 and 1980 elections might be a good place to begin.
.
correction to my @:59
should be "maintaining the current polling or *not much worse* by Election Day"
(point being that the polling may go down by 4-5 points and Obama is still likely to win, which is why Nate's model believes that one can say with 75% or so that the current polling will "hold up" to the extent of an Obama win).
While everyone appears to know the Rasmussen MO poll exists with McCain plus five, some of the answers in it are suprising as well. For one Bush got 48% fair or better approval raiting in the state. With 35% good or better. Still 52% poor, but drastically different than the national average, and interesting giving this Quibble string.
Second 50% stated Obama is too inexperienced to be president. While only 28% felt McCain was too old.
You should all take a look over there. Its only 500 voters so probably not great weight, but interesting none the less.
I prefer Obama to Hillary but she was stronger electorally. McCain was dead in Pennsylvania and Ohio, Hillary was winning Florida, she'd bring Arkansas and was very competitive in West Virginia. I know Barack is stronger in Colorado and Virginia but Hillary would have gotten a bump from winning the nomination too. She'd be up by 8-9 points right now. about 4 points better than Obama. Obama is a much riskier candidate. He can win, Hillary would win easily.
the other really interesting thing in this MO poll. 67% support drilling for oil, but only 54% believe this could improve the cost of gas. Interesting that 13-14% feel that drilling for oil is appropriate just to reduce dependancy by some margin, regardless of the price of gas.
I note you are still making trend adjustment numbers in all states. How does this work. It would seem the new polls in single states would be self adjusting to trends within the state and not blindly following the bump Obama got post primary. Or is the Trend adjusment something I just do not understand.
I guess the question really is why do trend adjustments still take place after new polls take place after the adjustment in trend was made? Or is this trend adjustment going to be a feature based only on new trends in National Polling? In other words now that Obama is down 1 to 2% this week in the trends will there be a negative trend adjustment to new polls to account for this?
Higgly:
trend adjustments work for individual polls.
A poll was taken in February. The trend then favored Obama. The trend adjustment gets the Obama numbers down.
A poll was taken in April. The trend then favored McCain. The trend adjustment gets the McCain number down.
It works out that we are still in an environment where trend adjustment, on the whole, tends to help Obama. But this may well change in a few weeks.
If you're going to try to incorporate all sorts of candidate-specific variables like party ID, incumbency, etc. and base your coefficients on historical elections data, you're likely to end up with something a lot like Ray Fair's presidential election predictor (at www.fairmodel.com). He's a Yale Economics prof who uses some pretty complex econometric modeling to isolate a set of variables -- some political, but mostly economic -- that he uses to predict the 2-party vote share for each candidate.
In my opinion, it's better to leave that kind of stuff to him and to devote this site instead toward detailed analysis of polls and the kind of predictive value they may have. Of course, there's some overlap if you're trying to determine whether some variables affect the predictive power of polling data, but as you said, the sample size problem makes it really difficult to say anything definitively about their impacts.
thanks anon at 2:30, I guess I just was not seeing the current trend as being either pro Obama or McCain, kind of stagnant lately, but that may just be a lack of polling. Can there be a trend absent polling?
When the economy's crappy, the incumbent party loses. It's pretty much that simple.
PPP is out with MO poll, showing McCain up!!!!!!!!!!!!
@ counsellorben: What a great paper you have linked to! Great information content, great analysis (in particular for somebody who has not followed previous elections in detail). Thanks a lot.
Nate: When looking at the paper's diagrams on poll movements for previous presidential elections, it appears that the majority of past elections have indeed displayed the 'regression-to-mean' pattern that you are applying to your projection. However, at least five of the last fourteen elections show a different pattern, which may be either described as "ever-widening lead', or as 'permanent advantage', or somewhere in-between those two. These were the elections in 1956 (Truman incumbent), 1964 (LBJ, post JFK), 1972 (Nixon incumbent), 1984 (Reagan incumbent) and 1988 (W. Bush, quasi-incumbent). The respective Wikipedia article suggests that the 1996 election (B. Clinton incumbent) has as well been of the 'permanent advantage' type: "Throughout the run-up to the general election, Clinton maintained comfortable leads in the polls".
In other words: You either have the (quasi-)incumbent advantage, in which he keeps a sustained and/or expanding lead, or a 'change' election that displays a 'regression-to-means' pattern and becomes a nail-biter in the end. While I was a bit sceptical about your 'regression-to-means' initially, after having looked at the data I now believe it is adequate and justified for 2008. However, there is no justification at all to apply an additional 'incumbency' correction to the data, in particular since McCain does not display any of the characteristics of an incumbent (presidential experience/ track record, power to implement pre-election etc.).
[This also shows how extra-ordinary the 2004 election has been. It has been the only election in the USA since pre-election polling exists, which the incumbent only won narrowly. All other incumbents were either defeated or won convincingly.]
Forgot to add that the 1984 (Reagan incumbent) election was also of the "sustained and/or ever-widening lead" type. That makes it seven of that type, out of the last fourteen
Hmm....
I built a simple Bayesian model, in which the "Macro" variables (incumbency, economy, etc.) predict the winner of the election as a prior Gaussian distribution with mean M and variance vM.
I then consider a poll taken t days before the election, with result P and variance vP + t*vT.
I get the following expected election result:
Most likely election result =
M * (vP + t*vT) / (vM + vP + t*vT)
+
P * vM / (vM + vP + t*vT)
Looking at the data from their paper, we can estimate that
vP / vM = 1/4
vT / vM = 1/112
vT / vP = 1/28
This corresponds very well to the time-evolution of their regression coefficient, and gives us an idea of the rate at which polling information decays. The amazing thing is that it suggests that the weight of the poll should be cut in 1/2 after four weeks, which is almost exactly what Nate uses for this site. However, it suggests that after 8 weeks, the weight of the poll should be 1/3, not 1/4.
Another interesting result is that the total variance of the poll equals the total variance of the Macro model about 12 weeks before the election. Before this, the model is more accurate, and afterwards the polls are.
Determining the intercept is a little bit trickier, but I think the data actually suggest that M is best interpreted as the expected two-way vote share of the incumbent, minus 49. If this is the case, then M should be roughly 3, meaning that the prior expected vote share for the incumbent party is about 52%. This is a very rough estimate, as the intercept data in their paper is a little weird. I suspect that this variable is more susceptible to short-term news events, such as conventions and debates.
I think the real lesson is that although this "Macro" models may be useful initially, there is still a lot of variance in these models and polls quickly become more important. Remember that in 2000, the models predicted that Al Gore would win in a landslide.
Obama electability:
I find it interesting that most major polls have Obama ahead by 3-5%--in a year where the democratic candidate should be ahead by 20%. The Bush administration and his republican cronies have so alienated the american electorate that there is no excuse why Obama shouldn't be outpolling McCain by considerably more than he is. Surely, the American electorate can't be duped again? Are there some other underlying reasons? Could his race be in issue? Unfortunately, racism is still alive and well in this country. Of course, very few voters will publicly admit that race will affect how they vote; but, once they are in the privacy of the polling booth, their deep rooted racial prejudices may indeed dictate how they ultimately vote. Case in point: I remember when Los Angeles Mayor Tom Bradley ran for Governor of California in 1982. On election day, he had a 7 percentage point lead which evaporate when all the votes were counted, and he lost the election....and that was even before the republicans learned how to steal elections. There may have been a number of variables in play, but race certainly was one. The Obama camp better hope he has at LEAST a 10% lead on election day. Otherwise he will be going in as a "president", and coming out as a "Senator."
The commonality of incumbent elections between 1956 and 1992 in which the incumbent won was that the incumbent never lost the polling lead in the 200 days before the election. In that light, it does not appear that McCain has much incumbent effect. In all other elections save Ford’s loss to Carter the lead changed hands in the last 120 days. This leads me to still have concerns with the projection methodology. I have less concern as we get closer to the election.
@Frank from Germany: "1956 (Truman incumbent)"
Something wrong here, since Eisenhower was the incumbent in 1956. What did you mean?
I'm not sure past elections are going to be that useful as a diagnostic framework. It would seem to me that spikes in approval rating towards the end of terms is due to nostalgia, and also due to the president fading from the scene.
I don't see that happening this time. The Bush aedifice is crumbling fast and he's going to be trying to spend much of the rest of his presidency trying to stack the deck against Obama, which one would expect the Dems will be watching for and publicising.
There will be far too much politics for the bounce to kick in.
The interesting thing is how the McCain = Bush meme will affect this.
Would tying Bush so tightly to McCain have an incumebncy effect on McCain making him stronger?
So how would you explain the Reagan wipe-out of carter despite the polls being pretty close to the last couple of weeks?
情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣用品,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,情趣,美國aneros,rudeboy,英國rudeboy,英國Rocksoff,德國Fun Factory,Fun Factory,英國甜筒造型按摩座,甜筒造型按摩座,英國Rock Chic ,瑞典 Lelo ,英國Emotional Bliss,英國 E.B,荷蘭 Natural Contours,荷蘭 N C,美國 OhMiBod,美國 OMB,Naughti Nano ,音樂按摩棒,ipod按摩棒,美國 The Screaming O,美國TSO,美國TOPCO,美國Doc Johnson,美國CA Exotic,美國CEN,美國Nasstoy,美國Tonguejoy,英國Je Joue,美國Pipe Dream,美國California Exotic,美國NassToys,美國Vibropod,美國Penthouse,仿真按摩棒,矽膠按摩棒,猛男倒模,真人倒模,仿真倒模,PJUR,Zestra,適趣液,穿戴套具,日本NPG,雙頭龍,FANCARNAL,日本NIPPORI,日本GEL,日本Aqua Style,美國WET,費洛蒙,費洛蒙香水,仿真名器,av女優,打炮,做愛,性愛,口交,吹喇叭,肛交,魔女訓練大師,無線跳蛋,有線跳蛋,震動棒,震動保險套,震動套,TOY-情趣用品,情趣用品網,情趣購物網,成人用品網,情趣用品討論,成人購物網,鎖精套,鎖精環,持久環,持久套,拉珠,逼真按摩棒,名器,超名器,逼真老二,電動自慰,自慰,打手槍,仿真女郎,SM道具,SM,性感內褲,仿真按摩棒,pornograph,hunter系列,h動畫,成人動畫,成人卡通,情色動畫,情色卡通,色情動畫,色情卡通,無修正,禁斷,人妻,極悪調教,姦淫,近親相姦,顏射,盜攝,偷拍,本土自拍,素人自拍,公園露出,街道露出,野外露出,誘姦,迷姦,輪姦,凌辱,痴漢,痴女,素人娘,中出,巨乳,調教,潮吹,av,a片,成人影片,成人影音,線上影片,成人光碟,成人無碼,成人dvd,情色影音,情色影片,情色dvd,情色光碟,航空版,薄碼,色情dvd,色情影音,色情光碟,線上A片,免費A片,A片下載,成人電影,色情電影,TOKYO HOT,SKY ANGEL,一本道,SOD,S1,ALICE JAPAN,皇冠系列,老虎系列,東京熱,亞熱,武士系列,新潮館,情趣用品,情趣,情趣商品,情趣網站,跳蛋,按摩棒,充氣娃娃,自慰套,G點,性感內衣,情趣內衣,角色扮演,生日禮物,生日精品,自慰,打手槍,潮吹,高潮,後庭,情色論譠,影片下載,遊戲下載,手機鈴聲,音樂下載,開獎號碼,統一發票號碼,夜市,統一發票對獎,保險套,做愛,減肥,美容,瘦身,當舖,軟體下載,汽車,機車,手機,來電答鈴,週年慶,美食,徵信社,網頁設計,網站設計,室內設計,靈異照片,同志,聊天室,運動彩券,大樂透,威力彩,搬家公司,除蟲,偷拍,自拍,無名破解,av女優,小說,民宿,大樂透開獎號碼,大樂透中獎號碼,威力彩開獎號碼,討論區,痴漢,懷孕,美女交友,交友,日本av,日本,機票,香水,股市,股市行情, 股市分析,租房子,成人影片,免費影片,醫學美容,免費算命,算命,姓名配對,姓名學,姓名學免費,遊戲,好玩遊戲,好玩遊戲區,線上遊戲,新遊戲,漫畫,線上漫畫,動畫,成人圖片,桌布,桌布下載,電視節目表,線上電視,線上a片,線上掃毒,線上翻譯,購物車,身分證製造機,身分證產生器,手機,二手車,中古車,法拍屋,歌詞,音樂,音樂網,火車,房屋,情趣用品,情趣,情趣商品,情趣網站,跳蛋,按摩棒,充氣娃娃,自慰套, G點,性感內衣,情趣內衣,角色扮演,生日禮物,精品,禮品,自慰,打手槍,潮吹,高潮,後庭,情色論譠,影片下載,遊戲下載,手機鈴聲,音樂下載,開獎號碼,統一發票,夜市,保險套,做愛,減肥,美容,瘦身,當舖,軟體下載,汽車,機車,手機,來電答鈴,週年慶,美食,徵信社,網頁設計,網站設計,室內設計,靈異照片,同志,聊天室,運動彩券,,大樂透,威力彩,搬家公司,除蟲,偷拍,自拍,無名破解, av女優,小說,民宿,大樂透開獎號碼,大樂透中獎號碼,威力彩開獎號碼,討論區,痴漢,懷孕,美女交友,交友,日本av ,日本,機票,香水,股市,股市行情,股市分析,租房子,成人影片,免費影片,醫學美容,免費算命,算命,姓名配對,姓名學,姓名學免費,遊戲,好玩遊戲,好玩遊戲區,線上遊戲,新遊戲,漫畫,線上漫畫,動畫,成人圖片,桌布,桌布下載,電視節目表,線上電視,線上a片,線上a片,線上翻譯,購物車,身分證製造機,身分證產生器,手機,二手車,中古車,法拍屋,歌詞,音樂,音樂網,借錢,房屋,街頭籃球,找工作,旅行社,六合彩,水噹噹,台中隆鼻,果凍隆乳,改運整型,自體脂肪移植,新娘造型,婚禮顧問,下川島,常平,常平,珠海,澳門機票,香港機票,貸款,貸款,信用貸款,宜蘭民宿,花蓮民宿,未婚聯誼,網路購物,婚友,婚友社,未婚聯誼,交友,婚友,婚友社,單身聯誼,未婚聯誼,未婚聯誼, 婚友社,婚友,婚友社,單身聯誼,婚友,未婚聯誼,婚友社,未婚聯誼,單身聯誼,單身聯誼,白蟻,白蟻,除蟲,老鼠,減肥,減肥,在家工作,在家工作,水噹噹,台中隆鼻,果凍隆乳,改運整型,自體脂肪移植,新娘造型,婚禮顧問,下川島,常平,常平,珠海,澳門機票,香港機票,貸款,貸款,信用貸款,宜蘭民宿,花蓮民宿,未婚聯誼,網路購物,婚友,婚友社,未婚聯誼,交友,婚友,婚友社,單身聯誼,未婚聯誼,未婚聯誼, 婚友社,婚友,婚友社,單身聯誼,婚友,未婚聯誼,婚友社,未婚聯誼,單身聯誼,單身聯誼,白蟻,白蟻,除蟲,老鼠,減肥,減肥,在家工作,在家工作,婚友,單身聯誼,未婚聯誼,婚友,交友,交友,婚友社,婚友社,婚友社,大陸新娘,大陸新娘,越南新娘,越南新娘,外籍新娘,外籍新娘,台中坐月子中心,搬家公司,搬家公司,中和搬家,台北搬家,板橋搬家,新店搬家,線上客服,網頁設計,線上客服,網頁設計,植牙,關鍵字,關鍵字,seo,seo,網路排名,自然排序,網路排名軟體,交友,越南新娘,婚友社,外籍新娘,大陸新娘,越南新娘,交友,外籍新娘,視訊聊天,大陸新娘,婚友社,婚友,越南新娘,大陸新娘,越南新娘,視訊交友,外籍新娘,網路排名,網路排名軟體,網站排名優化大師,關鍵字排名大師,網站排名seo大師,關鍵字行銷專家,關鍵字,seo,關鍵字行銷,網頁排序,網頁排名,關鍵字大師,seo大,自然排名,網站排序,網路行銷創業,汽車借款,汽車借錢,汽車貸款,汽車貸款,拉皮,抽脂,近視雷射,隆乳,隆鼻,變性,雙眼皮,眼袋,牙齒,下巴,植牙,人工植牙,植髮,雷射美容,膠原蛋白,皮膚科,醫學美容,玻尿酸,肉毒桿菌,微晶瓷,電波拉皮,脈衝光,關鍵字,關鍵字,seo,seo,網路排名,自然排序,網路排名軟體,英語演講,托福,Toastmaster,汽車借款,汽車借款,汽車借款,汽車貸款,汽車貸款,借錢,借貸,當舖,借款,借貸,借錢,週轉,
^^ nice blog!! ^@^
徵信, 徵信, 徵信, 徵信社, 徵信社, 徵信社, 感情挽回, 婚姻挽回, 挽回婚姻, 挽回感情, 徵信, 徵信社, 徵信, 徵信, 捉姦, 徵信公司, 通姦, 通姦罪, 抓姦, 抓猴, 捉猴, 捉姦, 監聽, 調查跟蹤, 反跟蹤, 外遇問題, 徵信, 捉姦, 女人徵信, 女子徵信, 外遇問題, 女子徵信, 徵信社, 外遇, 徵信公司, 徵信網, 外遇蒐證, 抓姦, 抓猴, 捉猴, 調查跟蹤, 反跟蹤, 感情挽回, 挽回感情, 婚姻挽回, 挽回婚姻, 外遇沖開, 抓姦, 女子徵信, 外遇蒐證, 外遇, 通姦, 通姦罪, 贍養費, 徵信, 徵信社, 抓姦, 徵信社, 徵信, 徵信公司, 徵信社, 徵信, 徵信公司, 徵信社, 徵信公司, 女人徵信, 外遇
徵信, 徵信網, 徵信社, 徵信網, 外遇, 徵信, 徵信社, 抓姦, 徵信, 女人徵信, 徵信社, 女人徵信社, 外遇, 抓姦, 徵信公司, 徵信社, 徵信社, 徵信社, 徵信社, 徵信社, 徵信社, 女人徵信社, 徵信社, 徵信, 徵信社, 徵信, 女子徵信社, 女子徵信社, 女子徵信社, 女子徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社,
^^ nice blog!! thanks a lot! ^^
徵信, 徵信社,徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 外遇, 抓姦, 離婚, 外遇,離婚,
徵信, 外遇, 離婚, 徵信社, 徵信, 外遇, 抓姦, 徵信社, 徵信, 徵信社, 徵信, 外遇, 徵信社, 徵信, 外遇, 抓姦, 徵信社, 征信, 征信, 徵信, 徵信社, 徵信, 徵信社, 征信, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信, 徵信社, 徵信社, 徵信社, 徵信, 外遇, 抓姦, 徵信, 徵信社, 徵信, 徵信社,
租車公司,行易花蓮租車旅遊網,花蓮,租車,花蓮,花蓮旅遊景點,花蓮,一日遊,一日遊,溯溪,賞鯨,泛舟,花莲租车,租车,花莲,花莲旅游,花莲租车,租车,花莲,花莲旅游,租车,花莲,花莲旅游,租车,花莲租车,花莲,花莲旅游,花蓮,花東,租車,花蓮,花蓮,旅遊,花東,租車,花蓮,花蓮,租車,花東,花蓮,旅遊,花東,租車,花蓮,旅遊租車,花蓮旅遊,花蓮租車,花東旅遊,花蓮租車,花蓮租車,花蓮旅遊,租車,花蓮旅行社,花蓮旅遊景點,花蓮旅遊行程,花蓮旅遊地圖,花蓮一日遊,花蓮租車,花蓮租車旅遊網,花蓮租車,花蓮租車,花蓮租車,花東旅遊景點,租車,花蓮旅遊,花東旅遊行程,花東旅遊地圖,花蓮租車公司,花蓮租車,花蓮旅遊租車,花蓮租車,花蓮旅遊,花蓮賞鯨,花蓮旅遊,花蓮旅遊,租車,花蓮租車,花蓮租車 ,花蓮 租車,花蓮,花蓮旅遊網,花蓮租車網,花蓮,租車,花東 旅遊,花蓮 租車,花蓮,旅遊,租車公司,花蓮,花蓮旅遊,花東旅遊,花蓮地圖,包車,花蓮,旅遊租車,花蓮 租車,租車,花蓮租車資訊網,花蓮旅遊,租車,花東,花東地圖,租車公司,租車網,花蓮租車旅遊,租車,花蓮,賞鯨,花蓮旅遊租車,花東旅遊,租車網,花蓮海洋公園,租車 ,花蓮 租車,花蓮,花蓮旅遊,花蓮租車公司,租車花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮包車,花蓮租車網,花蓮旅遊,花蓮租車,花蓮旅行社,花東旅遊,花蓮包車,租車,花蓮旅遊,花蓮租車,花蓮一日遊,租車服務,花蓮租車公司,花蓮包車,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮包車,花蓮租車網,花蓮旅遊,花蓮租車,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮租車,租車網,花蓮租車公司,花蓮旅遊,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮租車公司,花蓮一日遊,租車,租車服務,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮旅遊,花蓮賞鯨,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮包車,花蓮租車網,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,租車花蓮,花蓮租車,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,租車花蓮,花蓮租車,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮包車,花蓮,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮包車,花蓮租車,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮包車,花蓮租車,花蓮旅遊,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮包車,花蓮租車網,租車公司,花蓮租車,花蓮租車公司,花蓮一日遊,花蓮旅遊,花蓮旅遊租車,花蓮租車網,花蓮租車,花蓮一日遊,租車花蓮,花蓮租車,花蓮旅遊租車,花蓮租車,花蓮租車旅遊,花蓮租車,花蓮旅遊,花蓮旅遊,花蓮包車,花蓮溯溪,花蓮泛舟,花蓮溯溪,花蓮旅遊,花蓮旅遊,花蓮租車,租車公司,花蓮旅遊租車,花蓮租車,租車,花蓮旅遊,花蓮租車,花東旅遊,花蓮賞鯨,花蓮旅遊,花蓮泛舟,花蓮賞鯨,花蓮溯溪,花蓮泛舟,花蓮泛舟,花蓮溯溪,花蓮旅遊,花蓮旅遊,花蓮租車,花東旅遊,花蓮,花東,花蓮旅遊,花東旅遊,花蓮租車,花蓮,花東,花蓮旅遊,花蓮租車,花東旅遊,花蓮旅遊,花蓮租車,租車,花蓮旅遊,花蓮租車,花蓮旅遊租車,花蓮旅遊,花蓮租車,花蓮,花東旅遊萬事通,花蓮旅遊,租車,花蓮旅遊,花蓮租車,花蓮旅遊,花蓮租車,花蓮租車,花蓮租車,花蓮旅遊,花蓮租車,花蓮旅遊,花蓮租車,花蓮旅遊,花蓮租車,花蓮旅遊,花蓮租車,花蓮租車,花蓮包車,花蓮旅遊,花蓮租車,花蓮太魯閣,花蓮包車,花東旅遊,花蓮旅遊行程,花蓮旅遊,花蓮 租車,花蓮租車,花蓮租車旅遊,花蓮旅遊租車,租車,花蓮旅遊推薦,花蓮旅遊包車,花蓮租車,花蓮,花蓮租車,花蓮地圖,花蓮旅遊,花蓮旅遊資訊網,花蓮旅遊景點,賞鯨,花蓮旅遊行程,花蓮旅遊,花蓮旅遊租車,花東旅遊景點,花東旅遊行程,花蓮旅遊,花蓮租車,租車,花東旅遊,花蓮旅遊,花蓮租車,花蓮,旅遊達人,旅遊達人blog,花蓮租車旅遊資訊網,花蓮,租車,花蓮,花東旅遊,地圖,租車,賞鯨泛舟溯溪,租車,[ 芝麻店家 ] 花蓮租車旅遊資訊網,花蓮租車-花蓮旅遊租車資訊網 ,旅遊網,旅遊景點,花蓮行程,花蓮,花東,旅遊租車,旅遊,花蓮,租車,花東旅遊,花蓮租車旅遊,行易旅遊民宿資訊網,花蓮,旅遊,花蓮,一日遊,花蓮好玩的地方,花蓮,,一日遊,花東,租車,旅遊,花蓮旅遊,花東旅遊,花蓮租車,花蓮租車,花蓮旅遊-花東旅遊萬事通
艾葳酒店經紀公司提供專業的酒店經紀, 酒店上班小姐,八大行業,酒店兼職,傳播妹,或者想要到打工兼差、打工,兼差,或者八大行業,酒店兼職,想去酒店上班, 日式酒店,制服酒店,ktv酒店,禮服店,整天穿得水水漂漂的,還是想去制服店當上班小姐,水水們如果想要擁有打工工作、晚上兼差工作、兼差打工、假日兼職、兼職工作、酒店兼差、兼差、打工兼差、日領工作、晚上兼差工作、酒店工作、酒店上班、酒店打工、兼職、兼差、兼差工作、酒店上班等,想了解酒店相關工作和特種行業內容,想兼職工作日領、假日兼職、兼差打工、或晚班兼職想擁有快速賺錢又有保障的工作嗎???又可以現領請找專業又有保障的艾葳酒店經紀公司!
艾葳酒店經紀是合法的公司工作環境高雅時尚,無業績壓力,無脫秀無喝酒壓力,高層次會員制客源,工作輕鬆,可日領、現領。
一般的酒店經紀只會在水水們第一次上班和領薪水時出現而已,對水水們的上班安全一點保障都沒有!艾葳酒店經紀公司的水水們上班時全程媽咪作陪,不需擔心!只提供最優質的酒店上班,酒店上班,酒店打工環境、上班條件給水水們。心動嗎!? 趕快來填寫你的酒店上班履歷表
水水們妳有缺現領、有兼職、缺錢卡奴的煩腦嗎?想到日本留學缺錢嗎?妳是傳播妹??想要擁有高時薪又輕鬆的夜間兼職工作,打工機會和,假日打工,假日兼職賺錢的機會嗎??想實現夢想卻又缺錢沒錢嗎!??
艾葳酒店台北酒店經紀招兵買馬!!徵專業的酒店打工,想要去酒店的水水,想要短期日領,酒店日領,禮服酒店,制服店,酒店經紀,ktv酒店,便服店,酒店工作,禮服店,酒店小姐,酒店經紀人,
等相關服務 幫您快速的實現您的夢想~!!
艾葳酒店經紀公司提供專業的酒店經紀, 酒店上班小姐,八大行業,酒店兼職,傳播妹,或者想要到打工兼差、打工,兼差,或者八大行業,酒店兼職,想去酒店上班, 日式酒店,制服酒店,ktv酒店,禮服店,整天穿得水水漂漂的,還是想去制服店當上班小姐,水水們如果想要擁有打工工作、晚上兼差工作、兼差打工、假日兼職、兼職工作、酒店兼差、兼差、打工兼差、日領工作、晚上兼差工作、酒店工作、酒店上班、酒店打工、兼職、兼差、兼差工作、酒店上班等,想了解酒店相關工作和特種行業內容,想兼職工作日領、假日兼職、兼差打工、或晚班兼職想擁有快速賺錢又有保障的工作嗎???又可以現領請找專業又有保障的艾葳酒店經紀公司!
艾葳酒店經紀是合法的公司工作環境高雅時尚,無業績壓力,無脫秀無喝酒壓力,高層次會員制客源,工作輕鬆,可日領、現領。
一般的酒店經紀只會在水水們第一次上班和領薪水時出現而已,對水水們的上班安全一點保障都沒有!艾葳酒店經紀公司的水水們上班時全程媽咪作陪,不需擔心!只提供最優質的酒店上班,酒店上班,酒店打工環境、上班條件給水水們。心動嗎!? 趕快來填寫你的酒店上班履歷表
水水們妳有缺現領、有兼職、缺錢卡奴的煩腦嗎?想到日本留學缺錢嗎?妳是傳播妹??想要擁有高時薪又輕鬆的夜間兼職工作,打工機會和,假日打工,假日兼職賺錢的機會嗎??想實現夢想卻又缺錢沒錢嗎!??
艾葳酒店台北酒店經紀招兵買馬!!徵專業的酒店打工,想要去酒店的水水,想要短期日領,酒店日領,禮服酒店,制服店,酒店經紀,ktv酒店,便服店,酒店工作,禮服店,酒店小姐,酒店經紀人,
等相關服務 幫您快速的實現您的夢想~!!
酒店經紀人,
菲梵酒店經紀,
酒店經紀,
禮服酒店上班,
酒店小姐兼職,
便服酒店經紀,
酒店打工經紀,
制服酒店工作,
專業酒店經紀,
合法酒店經紀,
酒店暑假打工,
酒店寒假打工,
酒店經紀人,
菲梵酒店經紀,
酒店經紀,
禮服酒店上班,
酒店經紀人,
菲梵酒店經紀,
酒店經紀,
禮服酒店上班,
酒店小姐兼職,
便服酒店工作,
酒店打工經紀,
制服酒店經紀,
專業酒店經紀,
合法酒店經紀,
酒店暑假打工,
酒店寒假打工,
酒店經紀人,
菲梵酒店經紀,
酒店經紀,
禮服酒店上班,
酒店小姐兼職,
便服酒店工作,
酒店打工經紀,
制服酒店經紀,
酒店經紀,
菲
梵,
Post a Comment