participant.rb

  validates_presence_of :name, :if => :require_name, :on => :update
  validates_presence_of :email, :if => :require_email, :on => :update
  validates_presence_of :phone, :if => :require_phone, :on => :update

  def method_missing(name)
    if name.to_s =~ /require_\w+/
      project.present? && project.send(name)
    else
      super
    end
  end

participant2.rb

  validates_presence_of :name, :if => :require_name, :on => :update
  validates_presence_of :email, :if => :require_email, :on => :update
  validates_presence_of :phone, :if => :require_phone, :on => :update

  def require_name
    project.require_name
  end

  def require_name
    project.require_email
  end

  def require_email
    project.require_phone
  end

delegate is the right choice here, but if that wasn't an option, this would be my preferred refactoring:

[:name, :email, :phone].each do |attribute|
  define_method("require_#{attribute}") do
    project.send("require_#{attribute}")
  end
end