US elections

The data for previous early-election polls isn't exactly robust enough for us to attempt construction of such weights, so, instead, we'll be using an average measure with the number of observations acting as our weights. That way, we'll be able to account for standard deviations in the poll predictions, while smoothing out the differences and biases between various agencies' data.

For the purposes of this research, we've compiled a grand total of 241 polls that were released prior to the 2012 presidential election. For many of the states, we've managed to get enough data to limit the polls to April, May and June. However, there were more than plenty of states for which we were not at liberty to do so. For cases, where time-appropriate data was lacking, we'd widen the appropriate range by a distance of one month per every step - first including March and July, then February and August, then January and September. If even that was not enough to collect the number of polls we've set as acceptable - four - we'd look for data from back in 2011, which helped us fill a number of blanks, and then, finally, a data from October. While these are pretty significant methodological liberties, we will show in future analysis that the states for which the less appropriate data was used were not heavily affected by campaigning.

But, even with these assumptions and algorithmic data additions, some of the data is still lacking. For instance, three states - Alaska (eventually carried by Romney by 14 percent), Delaware (carried by Obama by 19 percent) and Wyoming (carried by Romney by 40 percent) had no polls conducted in them. There's a fair bit of sense in that - none of those states were believed to be potential battlegrounds at any point in the election (and, in fact, Romney's 14-point victory in Alaska can very well be regarded as a slight disappointment given the state's overall track record), all of them are worth the absolute minimum allotted amount of electoral votes and, as such, nobody campaigned in them. However, the absolute lack of data leaves us without options for including these three cases in the polling-based model.

There were also states that simply didn't have enough widely available data to make the «four polls» threshold - reliably red states Alabama, Oklahoma, Kansas, Idaho and Kentucky, blue states Vermont and Hawaii and the overwhelmingly Democratic Washington DC. However, for all of these, the data that is there appears to be reflective of the general situation and, if anything, the numbers for the states in question appear to produce more conservative margins of victory than seen in the actual election.

If we place Democratic and Republican polling advantages on the opposite sides of the spectrum - for instance, assigning «+» values to Obama's lead over Romney and «-» values in the opposite cases - the median value of the 48 observations is a 3-point lead for the Democratic party, made up from averaging the numbers from Colorado and Michigan. The most heavily Democratic subject is DC, which led in the polls by a whopping 80 percent. Out of actual American states, the most favorable to Democrats is Vermont with a 32-point advantage. For Republican leaning states, the biggest advantage was recorded in Utah - 42 percentage points.

Conversely, when polled advantage margins are taken as absolute values, regardless of whichever side has the lead, the median gap is 12 percent - beyond the threshold of what is usually considered a swing state. The smallest margin is recorded in North Carolina, while the top five of most closely-contested states is made up by the likes of Florida, Virginia, Colorado and Michigan - all regarded as important swing states.

The polling margin variable has a definite statistically significant relationship with actual election results. Its correlation with the 2008 election results has a Pearson's r of 0.942 and is significant on the 99% confidence level. Likewise, its correlation with the results of 2012 is significant on the very same level, with an r coefficient of 0.961.

To account for Alaska, Wyoming and Delaware, as well as other shortcomings of the poll data, we will introduce a secondary measure of an election's closeness, made up from results of previous elections in every given state. More specifically, we will take the three presidential elections that preceded 2012 - the infamous 2000 election, the 2004 election and the 2008 election - and construct a weighted average variable using the margins recorded in states in those elections.

The state-by-state results of the three electoral campaigns are heavily correlated, which each given pair recording a statistically significant Pearson's r of over 0.9. To form a singular variable, the results from the three elections will be taken with weights inversely proportional to their distance in years to 2012. As such, the 2000 election is assigned the weight of 0.1819, the 2004 election is assigned the weight of 0.2728 and the 2008 election will be entered under the weight of 0.5455.

The resulting variable is heavily correlated with our primary indicator of election closeness on poll data, but is also a very good predictor of the 2012 election outcome. The newly-created variable also clearly defined five closest battleground states of recent US history - Virginia, Colorado, Florida, Ohio and, shockingly enough, Missouri. The four former states lived up to their reputation during the 2012 election, producing four of the five smallest margins of victory of one major candidate over the other. The fifth, however, was seemingly not regarded as much of a battleground, as it received little campaign attention and was (correctly) believed to be a shoo-in for a Republican party victory.

The use of the two aforementioned methods of election closeness operationalization is consistent with the existing literature on the subject and appear to make up a reasonably foul-proof approach when used in conjunction. The idea to use these exact variables can be largely attributed to Virgil (2008). In that paper, the author makes a case for using the newly-emerging state-by-state polls for analyzing Electoral College effects in conjunction with past election results. In creating sets of models that use either past election results or polls, Virgil then compares the said models using the Bayesian Information Criteria and finds that they perform very similarly in terms of explaining the variance of the dependent variable. He also finds that the polls and past election results stack up differently on an election-by-election basis, which is what gives us the idea of use both of those measures, as they are readily available.

Having answered this operationalization question, we move our attention to the issue of actually measuring the distribution of campaign resource across states, to which there are several approaches and considered variables.

First and foremost, it would, at a quick glance, seem somewhat logical to use data on actual campaign spending in every given state that takes part in the election. However, while that data exists, it is not used or analyzed much when it comes to Electoral College research, for the simple reason that the goal of spending in a given state is usually not tied to attempting to acquire more votes in said state. While that previous statement might have held water a century ago, modern campaigns, tackling all sort of logistical and organizational issues, usually pay for services all across the country which will help across various states or the entire nation, but not necessarily the state in question. In other words, the simple, distilled measure of spending is just not appropriate for the goals set forth by this paper.

Indeed, there are measures that are much more obviously instinctively targeted at voters in a given standalone state. As our first measure of «campaign resource allocation» in this paper, we use the spending on television ads per capita in each given state by both campaigns.

The data in question is compiled by analysts at Kantar Media and is presented by major news source Washington Post. The overall level of TV ad spending for the 2012 election was, unsurprisingly, record-breaking at reached a stunning $900 million dollars from the two major campaigns and factually affiliated Presidential Action Committees.

The numbers presented by the Post reveal that the top ten states on ad spending received 78 percent of ad money in total, leading to a wide agreement in that the regular voters' exposure to political advertising differed greatly depending on their state of residence. Most of the campaign ad spending was local TV - national broadcast and national cable services received, in varying estimations, from five to fifteen percent of that.

The minimum amount of ad money received by a given state was shared by 16 different states in the 2012 election. And what was that amount? Zero dollars. Indeed, more than a third of eligible subjects in the United States were completely ignored by campaign ads - that number including the usual suspects in Alaska, Delaware, and Wyoming.

That number becomes a lot larger when one includes the states which had purely symbolic amounts of money spent on local ads. The mean value of per-capita standing across the 51 eligible subjects is three and a half dollars. For comparison's sake, Florida, which received the majority of ads, has seen 12 dollars per capita in spending. The somewhat contestable New Hampshire led the charge at 32 dollars, ahead of underpopulated potential swing states in Nevada and Iowa. In comparison, there were 20 additional states which saw ad spending below $0.05 per eligible voter. All of the distinctly red and distinctly blue states, as such, fell well into that category, in addition to some potentially close states like Arizona, Tennessee and Montana.

As a result, this creates a binary-like distribution for actual ad spending, with 35 states + DC getting from little to outright nothing in terms of ad spending. That is not to say that the remaining 14 states are interchangeable in regards to the amount of money spent - far from it - but they are leagues ahead of the funding that is received by states from the other category and can be lumped together by the sheer virtue of that alone.

The other indicator of campaign resource allocation is campaign visits. A candidate can only personally be in one place at a time and must choose his campaign stops carefully to have the best impact on his chances. Presidential candidates in the United States usually tend to favor a fairly hands-on approach to various campaign events and, in 2012, that was as true as ever, with the major players in the election recording a combined total of 988 visits to various events. The places where the candidates choose to visit get a great deal of free press for those visiting, and their choices of locations are often talked about and analyzed in great detail by pundits on national television, giving even more exposure to the candidates. The decisions on where to visit are handled very carefully by the candidates as they have a limited amount of time and energy.

The total count of 988 includes visits from Democratic incumbent Barack Obama and Republican candidate Mitt Romney as well as their significant others (Michelle Obama and Ann Romney respectively). The other key players included are vice-presidential candidates Joe Biden and Paul Ryan and their respective spouses.

It is worth noting that the dataset presented by Washington Post and Associated Press makes the distinction between strictly-campaigning appearances and fundraisers - appearances with the goal of adding to the campaign's budget through donations.

The state which saw the majority of campaign stops made in it was Ohio, with 148 points, while Florida and Virginia were a distant second and third with 115 and 98 respectively. For all of these states, the percentage of explicitly fundraising events in the overall amount of stops was less than 14%.

In comparison, most fundraiser visits were recorded in the heavily populated California, New York and Massachusetts - in all of these, fundraisers made up the majority of campaign stops and none of the three states were contested.

There were eight states that weren't visited by any of the senior campaign officials in the election - Alaska, Hawaii, Kansas, Maine, North Dakota, Rhode Island, Vermont and West Virginia. In addition to that, there were 11 states the campaign events in which were limited to only fundraisers - the most populated of them being Georgia. Meanwhile, Ohio, Florida, Virginia, Iowa and Colorado made up the top five states by non-fundraising visits, with Iowa also recording absolutely no fundraiser visits.

Incumbent candidate Barack Obama himself visited only 23 of the 50 American states on campaign trail, while Romney was a little more varied in his stops, attending campaign events in 33 states.

One might make an argument that stops in states like California and New York, traditionally blue states, help to disprove the theory that only battleground states matter. However, it should be noted that campaign stops in heavily populated states bring a lot of free publicity and promotional materials. These campaign stops are often huge events with thousands of people and when reported on, give the impression of overwhelming support for a candidate. In a way, these stops are just as much national advertisement as targeted ads might be, providing a wave of positive spin for the candidate to showcase in highlight reels and press releases.

Another reason there may be some outlying campaign visits to party loyal states is a strategic stop to help a struggling congress person win their race. In a state that a candidate is overwhelmingly popular in, a campaign stop with a senate candidate or House of Representatives candidate who is on the edge could make the difference in their election. Much more press and a larger crowd are just a couple of the benefits of such a stop for a struggling candidate trying to get their votes. We must remember that the democratic system of checks and balances makes it important for a president who wishes to keep all his promises to the voters to have his own party in control of the House and Senate. These kinds of campaign stops work best where a candidate has strong support. It's easy to see that while these kinds of states get more campaign visits, they don't get a proportional share of campaign dollars when it comes to advertising. In light of this it seems apparent that these stops do not disprove our theory.

The claim that the two aforementioned methods of selective presidential campaigning are significant and are utilized with the goal of drawing in votes in mind is not unsubstantiated. In Shaw (1999), the author analyzed three election cycles and found that both tv ads and appearances during presidential campaigning by the Republican candidate were statistically significant predictors of their share of the popular vote in the given state. It is also worth mentioning that their effect was especially notable when interacted with the percentage of undecided voters in the state in question.

We've previously discussed state election closeness as a factor in determining a given states propensity to receive campaign resources. However, there's a whole different aspect in the whole ordeal, which goes back to the previously discussed works of Banzhaf (1969) and Gelman and Katz (2001).

It would be preposterous to claim that a state's worth in the United States of America's presidential elections is down to just the closeness of the expected election race in that state because American states are also quite varied when it comes to their population sizes.

The average state or subject involved in the presidential election in 2012 had 4.7 million eligible voters. However, the distribution across all 51 of them is obviously uneven and, while the most populated state - California - had 29 million eligible voters, the least populated state - Wyoming, had around 1.5% of that or 66 times less.

The size of the state would not be a direct factor in a popular vote election - sure, one could potentially envision some indirect ways the size of a region would influence its electoral preferences and worth (for instance, they could, by default, have more exposure to electoral advertising or higher turnout due to population density and increased accessibility of voting booths). Those are just guesses and any sort of direct relation is hard to hypothesize.

Indeed, there would be no such topic of discussion when it comes to the Electoral College if the distribution of electoral votes were equal but, of course, as previously discussed, it's not. The two mandatory votes, which are added to the state's given proportional number (and, as such, put the minimum amount of votes per state at 3, not 1), make up, in total, 100 out of 538 votes overall. That proves to be more than enough to actually skew the proportionality.

For instance, while North Carolina gets approximately 2 electoral votes per million eligible voters, its' neighbor South Carolina gets 2.4. Neither of them are even particularly close to the minimum and maximum. Instead, the minimum is represented by two states with 15 million eligible voters each - Florida and New York - who both get 1.89 electoral votes per million. Meanwhile, the maximum is represented by Wyoming, which gets 6.84.

Predictably enough, the value of electoral votes per million voters is almost exactly inversely proportional to the actual population numbers, as the mandatory «+2» votes play a much bigger role in the smaller states.

In this paper, we will try to analyze the effect of this discrepancy in conjunction with the previously discussed conundrum of election «closeness». As previously stated, the mechanisms here are not clear - while Banzhaf's logic that the Electoral College favours big states (in that a decisive vote in a large state is much more worthwhile and is more likely to impact the election) has its definite logical merit, there's also the reverse mechanism of small states getting disproportionately large representation. It's a system that, conceivably, could see the effect vary from election to election depending on concrete conditions and anticipations.

For the purposes of gaging the distortions in campaign resource allocation, we will need a measure that would accurately account for potential distribution under the popular vote system. And, while correcting for eligible population in states appears to be sufficient at the first glance, one cannot deny that the states' political composition could be having a huge effect on resource allocation - after all, the candidates would probably prefer to spend more money in states where they could feasibly win more votes and there's probably some reason to the assumption that there are a lot more votes to play for in Ohio or Florida than Alabama or Vermont.

To account for this possibility, we will use Gallup's 2011 data on the political composition of the 50 states + DC. First and foremost, we will take Gallup's survey on US citizens' political party affiliations and use the percent of respondents who aren't registered with either party and don't admit to leaning either Republican or Democrat.

The mean percentage of «undecideds» across the 51 territories is 16, with a standard deviation of 2.5. The variance across states isn't really that noticeable, with the biggest value recorded in the small state Rhode Island at 24 and the smallest - in Washington DC at 10.

Gallup also present data on the voters' ideological preferences, grouping them into three categories - liberals, conservatives and moderates. «Liberals» is usually a term used to describe the Democratic party, while «conservatives» is usually reserved for Republicans. Gallup are quick to point out hat these terms are not interchangeable and that there are far more citizens who identify themselves as conservatives than liberals which is not reflected in the popular vote. However, even despite that, there are still high statistically significant correlations between the percent of conservatives and Republicans, as well as between Democrats and liberals.

The category that interests us most is «moderates», which should, by large, represent the percentage of people who presidential campaigns could have a feasible chance of persuading. The state-by-state share of moderates correlates with the amount of «undecideds» with a rather average r of 0.38. At the same time, that correlation is statistically significant.

As there is no definite way short of state-by-state polls (which are done by different agencies, combine all sorts of different methodology and are completely absent for some states) of measuring the amount of potential campaign targets in presidential elections, we will be using both of these variables in our models.

Apart from these variables that are essential for creating mathematical models relevant to our goals, we also include other control variables in various model specifications. These remaining control variables are:

· Gross State Product per capita - the indicator of a given state's economic output, it is usually a good measure of how economically successful a given region is, the GSP is also at least tangentially relevant to campaigning in that more successful states would be significantly more able to give large contributions to appealing campaigns.

· Campaign donations per capita - a monetary value of combined campaign contributions received in a given state and divided by the state population could act as a more direct way of measuring whether campaign contributions influence strategy. Indeed, it also falls under our understanding of campaigning as the offering of certain promises in exchange for voter resources - whether that be actual votes, donations or other activity.

There are more potential control variables, but they are ultimately less essential and their inclusion could clash with the inherently limited amount of observations. As such, further research with accounting for those factors or features could be made using a more generalized approach and with the inclusion of time-series data. For our dataset, we've made the decision to limit the amount of independent and control variables in models to five.

Research methods and methodological framework

Having discussed the data and the specific variables utilized in this paper, we move on to outlining the research methods, their implementation and the exact model specification.

It is important to note this research will operate within the realms of the positivist framework. It is the very reason why so much time was devoted to the operationalization of the relevant indicators and phenomena - so we could base the findings of this paper on observed empirical evidence and empirical approximations.

More specifically, we've decided not to stray from the customary norms of research in this field and, as such, will employ the rational choice theory as the basis of our methodology. The crux of the theory is that the individuals are assumed to have transitive and complete preferences, with the ranking of said preferences existing in independence from the set of preferences presented. The assumption of the fact that every actor is fully informed is not followed - instead, the actors are believed to be estimating the utility they'll get from adopting certain strategies and, as such, choose those which are expected to most adhere to their goals.

What were the goals of the actors in the 2012 election? Well, for the two main candidates in play for the presidency, there's a rather obvious answer - both were in it to win it. Even Romney who was, for the most part, the clear underdog in the fight for the presidency would undoubtedly prefer victory to any other realistic outcome and, even if he were faced with a high probability of losing, it's reasonable to assume he would want the margin that he lost by in regards to electoral votes.

Is it reasonable to assume that both campaigns primarily targeted maximization of the electoral vote tally? While electoral voters are the deciding factor in an election, one could argue that candidates don't really care about their margin of victory. That claim is certainly contestable but, even if this could be said for candidates who are sufficiently confident in their victory, the 2012 election really didn't seem to be a projected landslide victory going by the polls. Indeed, it didn't turn out to be one in the very end - Obama's winning margin proved to be lesser than that of the 2008 election and he carried a middling popular vote advantage of four percent.

Electoral campaigning is this paper is viewed as a means to an end - the end being victories. It is fair to say that we don't know which goals were pursued by the various three-party candidates in the 2012 election - they very well might have viewed themselves as potential victors, however small the odds, or they (most likely) pursued some sort of different aims that would be achieved with the help of the exposure that comes with presidential campaigning. It is possible their main goal was simply to be on a national stage steering the conversation to their causes in any way they could. In this example simply being a part of the race may have been a victory for them.

However, for the two prime campaigns, the goal in campaigning is securing electoral votes - and the goal in state-focused campaigning is, as such, securing the electoral votes in a given state, which means fighting for the majority of votes in that state.

Meanwhile, is the other side of the matter - voters - bound by rationality? In our eyes, there's a two-fold answer to this question. For why voters actually turn up to the electoral booths to cast their vote, we do not have an answer - we do not claim to have solved the famous voting paradox which stems from the free rider problem. At the same time, we do not claim voters are irrational in making the decision to vote.

We do assume rationality in the voters' decision to cast their vote for a certain candidate. Whatever motive drives them to support either Obama or Romney - be they issue voters, long-time party members or just people with matched personal value sets - we assume that their support is based squarely in rationality and stems from their set of preferences - all ranked differently for each individual.

Our research is also consistent with the principal-agent approach to elections. The politicians in our model acts as agents, who offer their approaches and sets of policies to the electorate, as well as their very services in implementing these approaches. The voters, meanwhile, are principals - they «hire» politicians with their votes and subsequently reward the quality of their work with the resources at their disposal - possible reelection, donations and mobilization, or, very well, impeachment or recalling. This view is consistent with previous research on the matter - for instance, Fearon (1999), where the author empirically demonstrates that the voters employ «selection» (more personality-based) and «sanctioning» (more policy-based) as the two main approaches to deciding on a vote and then evaluate politicians accordingly when they're in office.

We've went over the many variables and measures that will be used in modeling the research question in the given paper. Due to the varied nature of these indicators and their diverse range of characteristics, this paper will use several different methods of regression analysis to most accurately reflect the existing relationships between our variables.

The divided nature of the advertising variable has led us to the decision to interpret advertising as a binary variable. As such, we establish a certain threshold of «substantial advertising spending per capita» - the states that are above it will be considered to have received notable ad resources, while the states below it will be tagged as those who had disproportionately low resources assigned to them.

As advertising acts as our dependent variable, such model specification will require a method which deals with binary variables as outcomes. The most simplistic way of working with such data is the linear probability model, in which the Y in the model is the conditional probability of the event that specifies the binary variable. Unfortunately, the method in question is rather flawed - the model does not allow for the probability variable to be restricted between 0 and 1 (as probability should, generally speaking), which is indicative of a bigger issue - it assumes a bigger linear relation between the predictors and the estimated probability, which is not reasonable, as, with higher levels of probability, the «marginal effect» of X is logically supposed to decrease, not stay constant (Gujarati D., 2004).

Instead, the method utilized in this research for the aforementioned goals is logistic regression, more simply known as logit. The logit method circumvents the issues present in the linear probability model by measuring the outcome via the natural logarithm of the odds ratio.

In the formula presented above, L acts as the log measure of odds ratio and is the dependent variable of the model, calculated by taking the logarithm of the ratio between the probability of the «1» outcome and the probability of the «0» outcome. The coefficients, in this case, represent the change in the log odds ratio with the nominal increase of the value of the regressor.

The assumptions for the use and interpretation of the logit model are significantly lighter than the customary assumptions for Ordinary Least Squares models. First and foremost, the model has to be correctly specified - with sufficient predictors, whether interval, ordinal or nominal, and a nominal outcome variable.

The continuous predictors also have to be correlated with the logit of odds ratio and, as usual, potential multicollinearity should be accounted for.

There are specific statistics used to judge the performance of specified logit models. The most widely used and obvious one of them is the percentage of correct predictions of the dependent variable. The achieved percentage can be taken on its own as well as compared to percentages in other models - computing package SPSS, for instance, always produces the data for the model with only a constant and the dependent variable in question, which can serve as a solid comparison point for the start.

Outside of the simple measure of percentage, there are numerous ways to gage the model's predictive abilities. Many of them are dubbed as «pseudo» R-square measures, as they imitate the characteristics of the ever-familiar R² utilized in OLS models.

Among these measures is the frequently used Cox - Shell R^2, calculated as R2C-S = 1 - (L0 / LM) 2/n, where L0 is the likelihood function for the no-predictor model and LM is the likelihood function for the actual model. It's a reportedly effective measure and we'll be relying on it despite some apparent disadvantages, such as that the fact that it's upper bound could very well be significantly lower than 1 (Allison, 2013).

When it comes to goodness-of-fit estimates, literature suggests using multiple measures (Hosmer et al, 1997). In this paper, we will utilize Pearson's chi-square in conjunction with the Hosmer and Lemeshow test of goodness of fit - the use of the two should help us get a good grasp on the correctness of model specification.

In order to guard against the skewing of results due to overly influential data points, we will be using the widely-recognized Cook's distance as a measure of influence of given cases. This exact estimate has been selected due to its relatively easy computation and interpretation (the higher the value for a data point, the more leverage can be attributed to that exact data point). As suggested in Cook (1982), data points will be regarded as influential when the distance value for them surpasses 1.

Meanwhile, for continuous data on particular, we will first and foremost utilize visual ways of determining the nature of the relationship between the variables. Most notably, we will use locally weighted scatterplot smoothing known simply as the LOWESS method, which creates a curve that is separately fitted to specific segments of the data.

The use of LOWESS in revealing the nature of the exact relationship between the variables has been advocated in Cleveland (1979) and allows us to produce claims more substantial then those made after simply looking at the data.

Due to the heavy presence of heteroskedasticity of the errors in the attempted preliminary OLS-analysis, we will utilize heteroskedasticity-consistent (i.e. robust) estimators as described in Hayes and Cai (2007) for our analysis of visit data. As our analysis is done within the SPSS program which does not have robust regression hardcoded in, we make a particular note of using the authors' specifically-prepared macros for enforcing robust standard error estimation.

Meanwhile, for ad data, early analysis has allowed us to hypothesize that the relationship between election closeness and ad spending per voter is a function of gamma-like distribution. As such, we cautiously utilize the generalized liner model method with the assumption of a log link gamma response to test our hypotheses.

For all of our various dependent variables and methods, we will utilize four different sets of independent variables. Below, model 1 will stand for the use of the GDP measure, the donations data, the electoral vote proportionality, the poll projected value and the share of undecideds. Model 2 will replace undecideds with moderates, while model 3 will also make one change to model 1's specification - replacing the poll measure with the estimate based on previous years. Finally, model 4 will combine changes from models 2 and 3.

3. Findings

Effects on ad spending

The original idea for this paper was built on the presumption that candidates spend a lot in competitive states and less in decided states, yet, even with that preliminary hypothesis in mind, it appears we've vastly underestimated the sheer scope of this effect.

As previously noted, while electoral campaigns were expected to allocate their resources in linear fashion, they were instead found opting of an ultra-rationalistic approach. On a purely theoretical level, there is no need to campaign in a state that's already been won or lost - and it appears that the candidates were exceptionally well-aware of that.

Figure 1. Scatterplot of ad spending per voter on absolute poll margin, with LOWESS curve

As seen on the scatterplot of ad spending per eligible voter by the aggregate polling margin between the two major candidates (Figure 1), the spending outright ceased at around 8 percent, with state after state beyond that mark receiving either absolutely insignificant amounts of ad money or no ad money at all.

This early observation, should we be able to mathematically demonstrate it, could be crucial for the purposes of this paper as it displays that candidates use an extremely rationalistic mentality in targeting voters, meaning that a certain cut-off point in terms of projected margins is enough for a big chunk of the «potentially persuadable» population to be completely ignored during an election. The candidates do not have to account for their interests during campaigning and, as such, these voters have very little leverage over them.

Figure 2. Scatterplot of ad spending per voter on poll margin (Democrats - Republicans)

It is worth noting that the situation is not quite as clean-cut at the first glance as might be suggested. There are a couple of states that go against the trend - for instance, New Mexico, Minnesota and North Dakota received a lot more ad spending than would be reasonable in a purely rationalistic strategy based entirely on margins of victory. It's also worth noting that New Hampshire with its somewhat questionable status as a swing state was the record-setter in terms of ad spending per eligible voter, beating out the traditional likes of Florida and Ohio.

The whole picture gets a little clearer when the poll margins are taken into account with regards to the actual winning side. Going by the picture, the cutoff point for a state's inclusion into the campaign strategies of the two parties was different in regards to which party the state was leaning towards (Figure 2). With the exception of Oregon, most states that appeared leaning towards the Democratic party (who appeared to have a rather noticeable advantage in the polls overall) yet were feasibly in contention received plentiful ad spending. Meanwhile, states that appeared similarly close but leaning on the Republican side were largely ignored.

With that in mind, we move to calculating the results of the logit regression models, taking the dependent variable at «1» where the ad spending is substantial and at «0» where it's virtually non-existent. While the variance in substantial ad spending is huge, we find that there's enough of a gap between the values assigned to «0» and «1» to justify such categorization.

Out of the four logit models using a binary distribution for ad spending, the one that performs best includes the value constructed out of results from previous years and the share of moderates alongside GDP, donations and electoral votes (per capita, per capita and per million voters respectively). The model has a correct prediction percentage of 93.8, has a Cox-Snell pseudo R-Squared of.541 and is correctly fit according to both the chi-square test and the Hosmer - Lemeshow test.

The resulting empirical value of the model is:

The model was bootstrapped, creating 1000 samples to better estimate the significance of the coefficients. The coefficient has proved to be highly statistically significant in the case of the estimate on previous years, as well as statistically significant for the electoral votes proportionality measure, the GDP measure and the share of moderates - the latter have not been flagged as significant prior to the bootstrapping (Table 1).

Table 1. Coefficient estimators for logit regression analysis with binary value of ads as dependent variable