Question

Political advertising is often directed at winning over so-called swing voters, whose votes might go either way. Suppose that two political parties—the Freedom Party and the Liberty Party—disagree on whether to build a new road. Polling shows that of 1,000 total voters, 450 are firmly for the new road and 450 are firmly against the new road. Thus, each party will try to win over a majority of the 100 remaining swing voters.

a. Suppose that each party spends $5,000 on untargeted TV, radio, and newspaper ads that are equally likely to reach any and all voters. How much per voter will be spent by both parties combined?

b. Suppose that, instead, each party could direct all of its spending toward just the swing voters by using targeted social media ads. If all of the two parties’ combined spending is targeted at just swing voters, how much will be spent per swing voter?

c. Suppose that only the Freedom Party knows how to target voters using social media. How much per swing voter will it be spending? If at the same time the Liberty Party is still using only untargeted TV, radio, and newspaper ads, what portion of its total spending is likely to be reaching the 100, swing voters? How much per swing voter does that portion amount to?

d. Looking at your answers to part c, how much more per swing voter will the Freedom Party be spending than the Liberty Party? If spending per swing voter influences elections, which party is more likely to win?

Short answer

1. The combined spending on advertising per voter is $10.

2. The combined spending on social media advertising per swing voter is $100.

3. Freedom party’s spending per swing voter is $50.10% of the total spending of Liberty Party is likely to reach 100 swing voters. Spending per swing voter is $5.

4. Freedom Party spends $45 more than Liberty Party on an average swing voter.

The freedom party is more likely to win

Step-by-step solution

Explanation for part (a)

The combined spending per voter is calculated by dividing the total cost of untargeted advertising meant to influence all the voters by the total number of voters. This is calculated below:$$\begin{gathered} Combinedspendingpervoter=\frac{SpendingofLibertyParty+SpendingofFreedomParty}{TotalNumberofVoters} \\ =\frac{5000+5000}{1000} \\ =\$10 \end{gathered}$$

Thus, combined spending per voter is $10.

Explanation for part (b)

The combined spending per swing voter is calculated by dividing the total cost of targeted social media advertising meant to influence the swing voters by the total number of swing voters.This is calculated below:$$\begin{gathered} Combinedspendingperswingvoter=\frac{Spendingoflibertyparty+Spendingoffreedomparty}{Totalnumberofswingvoters} \\ =\frac{5000+5000}{100} \\ =\$100 \end{gathered}$$

Thus, combined spending per swing voter is $100.

Explanation for part (c)

Freedom party’s spending per swing voter is calculated by dividing their cost of targeted social media advertising meant to influence the swing voters by the total number of swing voters. This is calculated below:$$\begin{gathered} Spendingperswingvoter=\frac{Totalspendingontargetedadsbyfreedomparty}{Totalnumberofswingvoters} \\ =\frac{5000}{100} \\ =\$50 \end{gathered}$$

If the Liberty party is still using untargeted ads, it is spending a total of $5000. It's spending per voter, whether they are a swing voter or not, is $5, as shown below.$$\begin{gathered} Spendingpervoter=\frac{Spendingoflibertyparty}{Totalnumberofvoters} \\ =\frac{5000}{1000} \\ =\$5 \end{gathered}$$

Liberty Party’s total spending on 100 swing voters will be $500, calculated as follows:

10 % of the total spending of the Liberty Party ($5000) is spent on swing voters, which is $500.

The spending per swing voter will be $5, as shown below:$$\begin{gathered} Spendingperswingvoter=\frac{Portionoftotalspendingoflibertypartyonswingvoters}{Totalnumberofswingvoters} \\ =\frac{500}{100} \\ =\$5 \end{gathered}$$

Explanation for part (d)

Freedom party’s spending per swing voter is $45 (=$50-$5) more than the Liberty Party. If spending on swing voters affects the elections, the Freedom party is more likely to win the election as it spends $50 per swing voter compared to Liberty Party’s spending of $5 per swing voter.