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“Talk about extreme.” That was the response of Democratic presidential nominee Kamala Harris at September’s televised debate, after her rival, Donald Trump, made the baseless claim that migrants had been eating the dogs and cats of their neighbours in Springfield, Ohio.
Despite mounting criticism, Trump doubled down on the accusation. Likewise, during the more recent vice-presidential debate, Trump’s running mate, JD Vance, falsely claimed that the migrants in Springfield are illegal.
The arrival of hurricanes Milton and Helene then gave them more opportunities to disseminate disinformation. Trump’s team attacked the government over its response to the disaster, claiming that government money earmarked for disaster victims has been spent on migrants who crossed illegally into the US.
“Kamala spent all her Fema [Federal Emergency Management Agency] money – billions of dollars – on housing for illegal migrants”, Trump said at a rally in Michigan. This point was also repeated by Vance in an opinion piece on October 8 in the Wall Street Journal.
The claim is false. But does it make sense for Trump’s team to spread such extreme disinformation? Mathematical analysis suggests it can.
The positions of the candidates on the various issues, such as migration, can be represented on the political spectrum from the left to the right. It is fair to say that Trump places himself at the right end of the spectrum, while Harris sits at the centre.
If you are at the far end of the spectrum, left or right, then you want to move people as far in your direction as possible. So, given that these days, in the US at least, there appear to be no consequences for disseminating disinformation, you want your messages to be extreme.
By consistently hyping up the dangers of migrants, for example, more voters will start feeling that something needs to be done, even if they have never encountered an issue themselves.
Indeed, mathematical models show that the probability of a candidate positioned at the end of the spectrum winning an election can, at least theoretically, reach 100%, if the messages are nothing but extreme. The same does not apply to a candidate positioned in the middle.
We have seen this effect manifesting itself in the recent elections in Germany and France. Unless the public already has a strong appetite for the centre ground, which was the case for July’s general election in the UK, positions at the centre are often precarious.
The path to victory for Harris therefore remains steep. But there are means for an effective counteroffensive.
Clear communication
Political messages have two purposes: communicating where the candidate stands on the various issues, and making the voters feel that those positions are desirable. We can apply the mathematics of communication, which explains our cognitive response to digesting information, to infer the impact of political messages.
In particular, we can study how different messages on a given issue combine and interact. This, of course, only concerns voters who consume a variety of information sources, as opposed to those confined to an information echo chamber.
For those who consume both Democratic and Republican messages, the effect of combining them can be subtle. But, in many cases, they combine in an additive way with some weights on each message.
You can think of it as a weighted average of the two information sources. For example, if Harris says one thing and Trump says something opposite on a particular issue, then the net effect is each message muting the other slightly.
So, if Trump says the illegal Haitian migrants in Springfield are eating people’s pets, and Harris says the migrants are there legally and are not eating anyone’s pets, then people might come to the conclusion that, while there may be illegal Haitian migrants in Springfield, they may not be eating pets.
However, in some cases, one of the weights can take a negative value. This means that rather than adding them, the receiver of the two messages will subtract them. When this happens, the effect of that message is unexpectedly reversed.
For example, when clear and convincing evidence of the legal status of the migrants in Springfield is presented, the prevailing noise about their pet-eating habits will, if anything, strengthen people’s belief that the claim is false.
This can happen when the message from Harris is sufficiently loud and clear. Importantly, this does not mean Harris should loudly deny the disinformation. Provided that Harris sticks to her own messages in a clear and transparent manner, the mathematics of communication predicts that disinformation can turn itself against its spreader, for the following reasons.
The idea, roughly speaking, goes as follows. Suppose that a recipient of the messages is unaware of the prevalence of disinformation, and that there is a considerable gap between the unsubstantiated disinformation and reliable information, with the latter being communicated very clearly.
In this situation, communication theory shows that the receiver will dismiss disinformation more strongly than someone who is aware of the prevalence of disinformation.
It is reminiscent of the Japanese martial art judo where the ultimate aim is to use your opponent’s momentum, rather than your own force.
Disinformation should be challenged. And, indeed, both Harris and her predecessor Joe Biden have come out to condemn Trump’s “onslaught of lies” in relation to the two hurricanes.
But merely focusing on challenging disinformation is counterproductive. What is more important is for their own message to be communicated loud and clear.
No crystal ball can tell us whether the Democrats will retain the White House in November. But simply repeating the point that Trump is a threat to democracy, as Biden was prone to do, will not cut it.
Dorje C. Brody has received funding from UKRI.
