Extreme polarization of opinions fuels many of the problems facing our societies today, from issues on human rights to the environment. Social media provides the vehicle for these opinions and enables the spread of ideas faster than ever before. Previous computational models have suggested that significant external events can induce extreme polarization. We introduce the Social Opinion Amplification Model (SOAM) to investigate an alternative hypothesis: that opinion amplification can result in extreme polarization. SOAM models effects such as sensationalism, hype, or “fake news” as people express amplified versions of their actual opinions, motivated by the desire to gain a greater following. We show for the first time that this simple idea results in extreme polarization, especially when the degree of amplification is small. We further show that such extreme polarization can be prevented by two methods: preventing individuals from amplifying more than five times, or through consistent dissemination of balanced opinions to the population. It is natural to try and have the loudest voice in a crowd when we seek attention; this work suggests that instead of shouting to be heard and generating an uproar, it is better for all if we speak with moderation.