Equal dollar weighting puts, say, $10,000 into each of ten positions. It is the default in most retail portfolios and in many index products, and it is easy to explain to yourself.
What it does not do is equalise risk. If one holding has three times the volatility of another, it contributes roughly three times as much to portfolio-volatility for the same dollars. A "balanced" ten-name book can easily have half its daily swing coming from two names.
Example: $10,000 in a stock with 60% annualised volatility carries about $6,000 of annualised risk; $10,000 in one with 15% volatility carries $1,500. To make them comparable you need equal-risk-weighting or inverse-volatility-weighting instead. Equal dollars is a capital rule wearing a risk rule's clothes.
Related: equal-risk-weighting, concentration-risk