Encouraging Kindness in Rich People? Evidence presented in this video suggests that, statistically, rich people are more likely to be jerks than people with less money. How could this tendency be curbed, especially with regards to rich kids?
This is an interesting question as it has been of the opinion of many people around me that people who drive certain cars or are in a particular job or social status are selfish and don't care about anyone but themselves and maybe a little about those in their own circle of people.  But is this true?

TLDR - It seems to be true from studies presented, however there may be exceptions

For context, we need to define 'jerks' and 'rich' within the studies and the YouTube video you linked to (AppSCIENCE, 2018) had the studies and reports linked to it — NPR (2018), Piff, et al. (2012), Roberts &amp; Zarracina (2015) plus others — which backed their claims.

Rich (Definition)

Roberts &amp; Zarracina (2015) linked to the YouTube video talks of rich people being those who are


  at or near "the 1%" in wealth with an average income of $1M per year or more


some others would define it as someone who is substantially more financially well off and can include some below the top 1%.  My answer is based on this definition (see Social class, or socioeconomic status (SES) below).

Jerk (Definition)

The Oxford Living Dictionary defines Jerk as:


  A contemptibly foolish person


whilst the Urban Dictionary says 


  Jerks are selfish, manipulative bas****ds


but Piff, et al. (2012) linked to with the YouTube video talked about:


  how social class is associated with unethical behavior, or actions that harm others and are illegal or morally objectionable to one's community


with Social class, or socioeconomic status (SES) being:


  an individual's rank vis-à-vis others in society in terms of wealth, occupational prestige, and education (Adler et al. 2000)(Kraus, Piff, &amp; Keltner, 2011)


and there is a MacArthur scale of subjective SES which was used by Piff et al. (2012).

The evidence

Piff, et al. (2012) conducted 7 studies for their report


  In studies 1 and 2, upper-class individuals were more likely to break the law while driving, relative to lower-class individuals. In follow-up laboratory studies, upper-class individuals were more likely to exhibit unethical decision-making tendencies (study 3), take valued goods from others (study 4), lie in a negotiation (study 5), cheat to increase their chances of winning a prize (study 6), and endorse unethical behavior at work (study 7) than were lower-class individuals.


Roberts &amp; Zarracina (2015) covered the Washington Post story about water restrictions imposed in the wake of California's drought, and how wealthy people were reacting to them, along with research by Gillens &amp; Page (2014) and Page, Bartels, &amp; Seawright (2013) which were studying the political viewpoints of the elite.

The Washington Post story quoted a wealthy Californian resident to have said:


  I think we’re being overly penalized, and we’re certainly being overly scrutinized by the world," said Gay Butler, an interior designer out for a trail ride on her show horse, Bear. She said her water bill averages about $800 a month.
  
  It angers me because people aren’t looking at the overall picture," Butler said. "What are we supposed to do, just have dirt around our house on four acres?"


when talking about the fact that everyone had the same limit on water usage.  Defending the amount of water she and her neighbors "need" for their vast estates she also said:


  You could put 20 houses on my property, and they’d have families of at least four. In my house, there is only two of us,” Butler said. So “they’d be using a hell of a lot more water than we’re using.


Possible exceptions

On the other side of the spectrum, Rancho Santa Fe resident Randy Woods was feeling burdened by his lush landscape and opted to downsize. The 60-something chief executive of a biotech company moved a year ago from a two-acre estate — replete with two waterfalls, two Jacuzzis, a swimming pool and an orchard — to a condo in the tiny core of town known as “the Village.”

Woods said some of his friends would like to do the same, largely to cut down on their bloated water bills. But they have encountered an unforeseen obstacle, he said: The drought has dampened demand for large estates in San ­Diego County.  Another friend, Woods said, has seen the value of his nine-acre plot plummet from 30 million US Dollars to 22 million US Dollars.

So my question with those who are choosing not to sell because of drops in property value is, is this greed at play?  You could say that when you can still get $22M and therefore still live comfortably; plus Piff et al. (2012) states:


  Mediator and moderator data demonstrated that upper-class individuals’ unethical tendencies are accounted for, in part, by their more favorable attitudes toward greed.


Piff, et al. (2012) also highlights:


  significant philanthropy displayed by such individuals as Bill Gates and Warren Buffet


but the cynics would say that these people are motivated purely by self-interest rather than acting for honourable or unselfish reasons.  (They are doing it to look good and say "look at how thoughtful I am").

There are also likely to be instances of lower-class individuals exhibiting unethical tendencies, as research on the relationship between concentrations of poverty and violent crime indicates (Sampson, Raudenbush, &amp; Earls, 1997).

References

Adler, N. E., Epel, E. S., Castellazzo, G., &amp; Ickovics, J. R. (2000). Relationship of subjective and objective social status with psychological and physiological functioning: Preliminary data in healthy, White women. Health psychology, 19(6), 586.DOI: 10.1037/0278-6133.19.6.586

AppSCIENCE (2018). Are Rich People Worse Humans? (YouTube Video)Available at: https://www.youtube.com/watch?v=L90R6PtxFKE

Gilens, M., &amp; Page, B. I. (2014). Testing theories of American politics: Elites, interest groups, and average citizens. Perspectives on politics, 12(3), 564-581.DOI: 10.1017/S1537592714001595

Kraus, M. W., Piff, P. K., &amp; Keltner, D. (2011). Social class as culture: The convergence of resources and rank in the social realm. Current directions in psychological science, 20(4), 246-250.DOI: 10.1177/0963721411414654

NPR (2018). The Power Hour - Hidden Brain: A Conversation About Life's Unseen Patterns (Podcast)Available at: https://www.npr.org/2018/01/23/579976635/the-power-hour

Page, B. I., Bartels, L. M., &amp; Seawright, J. (2013). Democracy and the policy preferences of wealthy Americans. Perspectives on Politics, 11(1), 51-73.DOI: 10.1017/S153759271200360XFree PDF from: James N. Druckman, Department of Political Science, Northwestern University

Piff, P. K., Stancato, D. M., Côté, S., Mendoza-Denton, R., &amp; Keltner, D. (2012). Higher social class predicts increased unethical behavior. Proceedings of the National Academy of Sciences, 109(11), 4086-4091.DOI: 10.1073/pnas.1118373109

Roberts, D. &amp; Zarracina, J. (2015). Rich people are jerks, explained VoxAvailable at: https://www.vox.com/2015/6/16/8790357/rich-people-jerks

Sampson, R. J., Raudenbush, S. W., &amp; Earls, F. (1997). Neighborhoods and violent crime: A multilevel study of collective efficacy. Science, 277(5328), 918-924.DOI: 10.1126/science.277.5328.918