美国大学生数学建模大赛2009年MCM特等奖论文.doc

Political Advertising Budgeting for Obama 2012 Re-electionSummary To specify the problem, we consider the situation the Obama campaign meets to prepare for the 2012 re-election. The total 91 million US dollars campaign funds is distributed to two aspects：the new media Internet and political activities. We use the Analytical Hierarchy Process method to obtain the investment the Obama campaign should pour into the major Internet companies. The weight each company owns is in proportional to the expenditure the campaign spent on them in 2008. We conclude that a total 7million US dollars should be prepared for the Internet, of which 5 million is directly spent and the remaining 2 million incremental budgeting is for special situations.As for the political activities, the number of electoral votes awarded to each state is the main factor in our model. Considering the previous elections, there are states tend to support the Democratic Party or the Republican Party. This is relatively convenient for us to model the expenditure distributed to each state because some states are of small probability for the Democratic Party to fight for. We do not take into account the 8 states which strongly support the Republican Party in previous elections. In the remaining 42 states and the Dist. of Columbia, we design a rank-oriented method to distribute the remaining 84 million dollars; the arrangement for each state is presented in this paper.1 Introduction In the US history, each candidate has a electoral team aimed at winning the battle for the presidential election. Before the primary election, team members will collect a large amount of information to analyze the electoral situation of every state so as to know the measures they should take in each state respectively. Considering a specific state, whether it applies the proportional or the “winner-takes-all” system affects the election greatly. How to spend the campaign funds depend to a large extent on the number of electoral votes awarded by the state.To be specific, we assume the candidate to be the incumbent US president Barack Hussein Obama and budget the campaign funds for his 2012 re-election. Since Obama represents the Democratic Party, our model aims at helping the Obama campaign win the battle against the Republican Party. In the last ten elections, 4 states of 56 electoral votes support the Democratic Party strongly; 8 states of 36 electoral votes support the Republican Party, including Nebraska which takes the proportional system. We have 19 states of 214 electoral votes tend to support the Democratic Party and 14 states of 145 electoral votes tend to support the Republican Party. The other 6 states of 87 electoral votes are not sure which party to support. From this perspective, the Democratic Party has advantage over the Republican Party. However, the competitor will implement his strategy to fight for the presidential position. A successful arrangement should take dynamic factors into consideration. 2 AssumptionsWe assume that the increased voters after the political policies implements is directly proportional to the expenditure spent in a certain state. The higher the click of the political advertisements is, the greater the influence of the political advertisement is.The impact of Internet on the presidential election has limitations, so unlimited expenditure on the Internet will not work efficiently. Whether the Democratic Party or the Republican Party reaches a specific state earlier does not influence the effectiveness of online political advertisements. 3 Model EstablishmentTo refine the problem, we consider budgeting the campaign funds to help the incumbent US president Barack Hussein Obama win the 2012s re-election. Taking a look at his preparation for the 2008 presidential election, we find that media and political activities play a considerably important role. Except for traditional media advertisements, we budget the campaign funds from two aspects: The nationwide Internet. According to surveys, the key point that brings Obama to a total success in the 2008 US presidential election is that the campaign makes full use of the Internet. So a large amount of the campaign funds should be poured into political advertisements on the Internet. The traveling expenditure spent in each state. To get the support of a specific state, the candidate must go for political speeches and a series of other political activities in that state. The travel to the state costs a proportion of the total campaign funds.To present a successful budgeting, we should take into account the factors concerning the Internet and the travels to each state. 3.1 The Influence of the Internet According to statistics, an approximate 85% of the electoral funds collected by the Obama campaign are from the Internet; and the major parts include search engine, online advertising, network community and media and newspaper network. We use the Analytical Hierarchy Process to determine the influence of search engine, online advertising, network community and media and newspaper network on the effectiveness of online political advertisements. The grade classification is shown in Figure 1.Effectiveness of Online Political Advertisements Media and Newspaper Network Network CommunityOnline Advertising Search Engine GYMCeBFCPTG: Google; Y: Yahoo; M: Microsoft;Ce: Centro; B: Broadband; F: Facebook; C: CommunityConnect;P: Politico; T: Turner. Figure 1 The Grade Classification of Online Political Advertisements According to our assumptions and the actual case of the Internet, the Obama campaign should pay each net company based on the click on the Internet. Basically, the expenditure of the 2008 election spent on each part can be used to estimate the ratio of campaign funds that should be poured into these Internet companies. However, as the Internet industry develops, the weight of each Internet company will change. We treat as search engine, as online advertising, as network community and as media and newspaper network. Now we investigate the influence of them on the object, the effectiveness of online political advertisements. Let be the ratios of the importance of to the importance of . Since the expenditure the Obama campaign spent on search engine, online advertising, network community and media and newspaper network are，, and,respectively. We combine it with the Saaty Rule, and take ，. The Comparison Matrix is then obtained as fallows:The maximal characteristic value of the Comparison Matrix is; thereby the consistency index of Matrix is obtained as. Since the random consistency index of a four-order matrix is, the random consistency index ratio of Matrix is. The result is acceptable. The corresponding normalized characteristic vector is , which is taken as the weight vector of the four factors. 3.1.1 The Influence of Search Engine on the Object Table 1 presents the report on share of search engine in the US market released by the Market Statistic Company of America: Table 1 Share of Search Engine in the US Market We know from Table 1 that Google, Yahoo and Microsoft almost dominate in the market share. So the normalized market share ratios of the three search engines, , and, can be used as the weight of them; therefore the weight vector of the three search engines to the object can be obtained as .3.1.2 The Influence of Online Advertising on the Object The United States has two main online advertising companies: Centro and Broadband. In the year 2008 the Obama campaign spent and on them respectively. The weights of the two companies on the object are correspondinglyand. So the weight vector of the two companies to the object is.3.1.3 The Influence of Network Community on the Object The 2008 Obama campaign totally spent andon the two major network communities Facebook and CommunityConnect. In the same manner, the weights of the two network communities on the object are and.We obtain the weight vector of the two network communities to the object as.3.1.4 The Influence of Media and Newspaper Network on the Object The expenditure the Obama campaign spent on the two main media and newspaper network Politico and Turner areand. We assume that the weights of the two networks on the object areand; so we obtain the weight vector of the two networks to the object as.According to the related US regulations, a candidate cannot accept the donation from individuals any more once he receives the government funding. That is, all the campaign funds except for the government funding should be collected before the government funding reaches him. Once he declares to accept the government funding, the campaign should try their best to accomplish the main task of attracting voters. They need to increase the input in the Internet in the process of tracing more voters.The Obama campaign spent approximately8,000,000 on the Internet in 2008, of which3,000,000 is spent from January to July. The expenditure spent after July is approximately3,000,000, which accounts for 3/8 of the total amount spent on the Internet. We find that the Obama campaign collected a total amount of650,000,000 funds in the 2008 election, of which is from the Internet; that is an amount of 514,250,000. Since the Obama campaign plans to collect1 billion funds for the 2012s election, an increase ofcompared to the year 2008, we assume a same ratio of that will be from the Internet; that is850,000,000. A rough calculation of the expenditure that should be invested in the Internet is million US dollars. After accepting the government funding, the input in the Internet is approximatelymillion dollars. This is the basic investment in the Internet during the later months; it doesnt allow for accidental situation that may occur. The expenditure the competitor John McCain spent in the 2008s election is far less than Obama. So the Republic Party must have realized the importance of the Internet in the election, thus increasing the investment in the Internet in the same manner. Considering this situation, an expenditure of 5 million will hardly reach the anticipation. An additional investment should be prepared in the combat with the competitor. It is difficult to predict how much the competitor will add to invest in the Internet. So it will be hard to determine the additional expenditure the Democratic Party should pour into the Internet in order to increase competitiveness. Note that the Internet has its limitations: it will be useless to increase the investment in the Internet unlimitedly. We prepare another2 million for later election. Considering the determined 5 million, a total investment of 7million will be enough for the later three months. To obtain the investment in each company, we divide the total5million to each company according to the weight of each company in the effectiveness of online political advertisements. The results are shown in Table 2. Table 2 The expenditure the Obama campaignshould invest in Internet companyInternet CompanyInvestment (US Dollars )Google2,294,000Yahoo571,000Microsoft398,000Centro957,000Broadband149,500Face book152,500Community connect87,500Politico269,000Turner123,000It lasts approximately 14 weeks from the time the campaign receives the government funding to the election. Table 2 presents the expenditure the Obama campaign should invest in each Internet company. If they are divided by 14, the corresponding average investment the Obama campaign should invest in each Internet company can be obtained. The remaining2 million is distributed as an incremental budgeting to each Internet company according to the effectiveness of online advertisements. 3.2 The Influence of Political ActivitiesSince the electoral votes are awarded to each state based on the total population, some states are awarded more electoral votes than other states. Taking California as an example, it has 54 electoral votes, which is far more than that of other states. So they will be paid more attention to in the election. According to the latest population census of the United States in 2010, the electoral votes should be re-awarded because the ratios of the population in each state have altered. The new distribution of electoral votes awarded to each state is shown in Table 3. (The Dist. of Columbia has 3 electoral votes.)Table 3. The new distribution of electoral votes awarded to each state CA54NJ14AL9IA6ME4TX38VA13CO9KS6NH4NY30AZ12MN9MS6RI4FL29WA12SC9NV6MT3IL20IN11KY8UT6AK3PA20MA11LA8NE5DE3OH18TN11CT7NM5ND3GA16MD10OK7WV5SD3MI16MO10OR7HI4VT3NC15WI10AR6ID4WY3In preparation for the election, a candidate will not go to every city because time and expenditure do not allow him to go to all the states. The campaign will previously determine which states the candidate need to go.It is strategic to arrange a series of political activities for the presidential election. The previous strategy on the Internet is mainly aimed at awaking the public to participate in the presidential election. It is designed to attract more citizens to be voters. However, whether they will support the Democratic Party or the Republican Party remains a question. Since election is a two-side battle, either campaign cannot consider itself only. The policies the competitor implements should have impact on the other campaign. So the two sides will alter their strategy continually. Political activities are to some extent bridges to attract the public to participate in government affairs and to establish a better image of the government. What the candidate should take into account is that the political policies the competitor will implement.Firstly, we classify the 50 states and Washington D.C. according to the previous election results: states that support the Democratic Party, states that support the Republican Party, states that tend to support the Democratic Party, states that tend to support the Republican Party, and states that are not certain which party to support. The classification is presented in Table 4.Table 4 The tendency to support the Democratic Party or the Republican Party in the presidential election States and the electoral votes awarded Support the Democratic Party(4 states 56 electoral votes )HI 4; NY 30;MA 12; MD 10Support the Republican Party(8 states 36 electoral votes)ID 4; WY 3; UT 5; AK 3; SD 3; NE 5; KS 6;OK 7Tend to support the Democratic Party(19 states 214 electoral votes)OR 7; CA 54; MI 16;